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An Experimental Evaluation of the Application of Smart Damping Materials for Reducing Structural Noise and Vibrations Kristina M. Jeric Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science In Mechanical Engineering Mehdi Ahmadian, Chair Harley H. Cudney, Daniel J. Inman April 23, 1999 Blacksburg, Virginia Keywords: Structural Vibration, Piezoceramic, Piezoelectric, Passive Damping, Shunt Circuits, Vehicle Noise, Structural Noise Copyright 1999, Kristina M. Jeric

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Page 1: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

An Experimental Evaluation of the Application of Smart DampingMaterials for Reducing Structural Noise and Vibrations

Kristina M. Jeric

Thesis submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Science

In

Mechanical Engineering

Mehdi Ahmadian, Chair

Harley H. Cudney,

Daniel J. Inman

April 23, 1999Blacksburg, Virginia

Keywords: Structural Vibration, Piezoceramic, Piezoelectric, Passive Damping, Shunt Circuits, Vehicle Noise, Structural Noise

Copyright 1999, Kristina M. Jeric

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An Experimental Evaluation of the Application of Smart Damping Materialsfor Reducing Structural Noise and Vibrations

Kristina M. Jeric

(ABSTRACT)

This study evaluates the application of smart damping materials for reducing structuralnoise and vibrations. The primary purposes of this study are to:

1. Explore the feasibility of smart damping materials, such as piezoelectricmaterials, for augmenting and improving the noise and vibration benefits ofpassive damping materials and

2. Provide a preliminary evaluation of the noise and vibration benefits, andweight savings of smart damping material as compared to conventionaldamping treatments.

To achieve the objectives of the study, a special test rig, designed to measure bothvibrations and structure-borne noise of a test plate, was constructed and validated in theearly stages of the study. Upon validating the test rig and the instrumentation that was setup for data collection and processing, a series of tests were performed. The tests wereintended to establish a baseline for the test rig and compare the performance of smartdamping materials with a number of passive interior automotive treatments. Further, inorder to evaluate the effect of smart damping materials on the sound transmission loss, aseries of tests were conducted according to the SAE J1400 test specifications. The testsevaluate the transmission loss for smart damping materials for an undamped and adamped plate.

The passive damping technique used for this study involved attachingpiezoelectric patches with resonant electrical shunts. The vibration modes of the platewere determined both analytically and experimentally, using laser measurementtechniques, in order to determine effective placement of the piezoceramic materials.Three piezoceramic patches were applied to control four structural resonance frequenciesof the plate.

The tests show that smart damping materials have substantial performancebenefits in terms of providing effective noise and vibration reduction at a frequency rangethat is often outside the effective range of passive damping materials. Further, judging bythe acceleration and noise reduction per added weight, the test results indicate that smartdamping materials can decrease the vibration peak of a steel plate at 151 Hz by up to16.24 dB with an additional weight of only 0.11 lb. The addition of constrained-layerdamping (CLD) can decrease that same peak by 18.65 dB, but it weighs 10 times more.This feature of smart damping materials is particularly useful for solving particular noiseor vibration problems at specified frequencies, without adding any weight to the vehicleor changing the vehicle structure.

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Acknowledgements

The successes of this project have been the result of tireless efforts on the part of many at

Virginia Tech and Lear Corporation. First, I would like to thank my advisor and mentor,

Dr. Mehdi Ahmadian, for all his time, effort, encouragement, and enthusiasm throughout

my graduate studies in the Mechanical Engineering Department. I would also like to

thank Drs. Daniel J. Inman and Harley C. Cudney for serving on my graduate committee.

The financial and technical support provided by Lear Corporation is greatly

acknowledged. In particular, I am indebted to Dr. Barry Wyerman who provided much

of the materials that we needed for the tests, as well as practical insight and many useful

suggestions for conducting the tests. I am grateful for all the help provided by Messrs

Mark ZumMallen, John Gores, and Kevin Stone during the transmission loss tests at Lear

Corporation. Additionally, the generous donations by 80/20 and PCB Piezoelectronics

Inc. made the successful completion of this research possible.

I would also like to greatly acknowledge the technical and design support of Dr.

Robert West, Dr. Chul Hue Park, Dr. David Coe, Mr. Mark McEver, Mr. Chris Hobbs,

and the Machine Shop Personnel at the Department of Mechanical Engineering.

The support provided by the Advance Vehicle Dynamics Laboratory (AVDL) and

the Center for Intelligent Material Systems and Structures (CIMMS) at Virginia Tech

throughout the course of this study is also greatly acknowledged.

Finally, I would like to express my appreciation to my parents, Anthony and

Rosemarie Jeric, and my brother, Steve, for their endless love and support during my

years at Virginia Tech. Their love, as well as the camaraderie of many good friends,

made this journey absolutely wonderful.

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Contents

1 Introduction…. .................................................................................................... 1

1.1 Introduction ............................................................................................. 1

1.2 Research Objectives................................................................................. 2

1.3 Approach ................................................................................................. 3

1.4 Outline……. ............................................................................................ 3

2 Background…. .................................................................................................... 4

2.1 Piezoelectric Theory................................................................................. 4

2.2 Applications for Piezoceramics ................................................................ 5

2.3 Literature Search...................................................................................... 6

2.3.1 Control of Structural Noise and Vibration with Smart Materials .. 7

2.3.2 Vehicle Vibration and Noise Control Using Smart Materials ........ 8

2.3.3 Increasing Transmission Loss with Piezoceramics........................ 8

2.3.4 Passive Damping Using Shunted Piezoceramics ........................... 9

2.4 Shunt Circuit Design.............................................................................. 12

2.4.1 Shunt Tuning ............................................................................. 14

2.5 Summary................................................................................................ 17

3 Experimental Setup ........................................................................................... 18

3.1 Test Stand Design .................................................................................. 18

3.1.1 Bottom Box Enclosure................................................................ 19

3.1.2 Top Box Enclosure ..................................................................... 22

3.1.3 Excitation Frame ........................................................................ 22

3.1.4 Electromagnetic Shaker .............................................................. 25

3.1.5 Total Test Stand Assembly ......................................................... 25

3.2 Test Setup .............................................................................................. 26

3.2.1 Test Plate Setup.......................................................................... 26

3.2.2 Transducer Arrangement ............................................................ 28

3.2.3 Data Acquisition System ............................................................ 28

3.3 Validation Tests ..................................................................................... 30

3.3.1 Vibration Response Validation ................................................... 30

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3.3.2 Acoustic Response Validation .................................................... 33

3.3.3 Repeatability and Linearity......................................................... 34

3.4 Summary…............................................................................................ 36

4 Baseline Tests and Smart Plate Development..................................................... 37

4.1 Baseline Tests ........................................................................................ 37

4.2 Test Plate Vibration Characteristics........................................................ 37

4.2.1 Test Plate Resonance Frequencies .............................................. 38

4.2.2 Test Plate Mode Shapes.............................................................. 38

4.2.2.1 Analytical Mode Shapes.............................................. 38

4.2.2.2 Experimental Mode Shapes......................................... 40

4.3 Test Plate Acoustic Characteristics......................................................... 43

4.4 Smart Plate Development....................................................................... 46

4.4.1 PZT Placement and Application ................................................. 46

4.4.2 Attaching PZTs to Structures...................................................... 47

4.4.3 Smart Damping Plate Test Setup ................................................ 49

4.5 Summary................................................................................................ 50

5 Smart Damping Test Results and Benefits ......................................................... 51

5.1 Vibration Benefits of Smart Damping for Undamped Plates................... 52

5.1.1 Third-Octave Analysis................................................................ 50

5.2 Acoustic Benefits of Smart Damping for Undamped Plates.................... 55

5.2.1 Third-Octave Analysis................................................................ 57

5.3 Benefits of Smart Damping for Damped Structures................................ 61

5.3.1 Vibration Benefits of Adding Smart Damping to

Damped Structures ..................................................................... 62

5.3.2 Acoustic Benefits of Adding Smart Damping to

Damped Structures ..................................................................... 65

5.4 Weight Saving Benefits of Smart Damping Materials............................. 68

5.5 Summary................................................................................................ 73

6 Transmission Loss Tests.................................................................................... 74

6.1 Test Setup .............................................................................................. 74

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6.2 Transmission Loss Calibration Tests ...................................................... 75

6.3 Transmission Loss Testing and Results .................................................. 77

6.3.1 Tuning the PZT Shunts............................................................... 77

6.3.2 Transmission Loss Test Results .................................................. 79

6.4 Summary................................................................................................ 83

7 Conclusions…. .................................................................................................. 85

7.1 Summary................................................................................................ 85

7.2 Recommendations for Future Research .................................................. 85

References……………………………………............................................................... 87

Appendix A…………………………………................................................................ A1

Appendix B…………………........................................................................................B1

Appendix C…………………… ....................................................................................C1

Appendix D……………. ............................................................................................. D1

Vita……………………………………………………......................................................

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List of Figures

2.1 Basics Symbols and Terminology in Piezoelectricity ........................................... 5

2.2 Literature Search Flowchart................................................................................. 7

2.3 Shunt Circuit Design Concepts Used by Hagood and Wu .................................. 10

2.4 Shunting of Piezoelectric Materials (Single Shunt) ............................................ 12

2.5 Operational Amplifier Circuit Emulating a Variable Inductance ........................ 13

2.6 Experimental Shunt Circuit Board ..................................................................... 14

2.7 Single Shunt Circuit and Power Supply Configuration ...................................... 14

3.1 Vibration and Acoustics Test Stand Schematics................................................. 19

3.2 Frame for Bottom Box Enclosure....................................................................... 20

3.3 Section View of Bottom Box Enclosure Side..................................................... 21

3.4 Front Side of Bottom Box Enclosure with Door................................................. 21

3.5 Inside of Reception Chamber............................................................................. 22

3.6 Excitation Frame ............................................................................................... 23

3.7 Excitation Frame Mount to Bottom Box ............................................................ 24

3.8 Clamping Frame on Excitation Frame................................................................ 24

3.9 Electromagnetic Shaker and Stinger Rod Assembly........................................... 25

3.10 Total Test Stand Assembly ................................................................................ 26

3.11 Standard Test Plate in Testing Position .............................................................. 27

3.12 Acoustic Barrier Arrangement ........................................................................... 27

3.13 Microphone Placement in the Reception Chamber............................................. 28

3.14 Shaker Table Test Stand and Data Acquisition Schematic.................................. 29

3.15 Periodic Chirp Signal Generated by HP Analyzer .............................................. 30

3.16 Frame Acceleration Response without Test Plate Installed................................. 31

3.17 Effect of Test Plate on Frame Acceleration Response ........................................ 32

3.18 Sample Frequency Response Function Data for Standard Test Plate .................. 32

3.19 Sample Sound Pressure Levels with and without Plate....................................... 33

3.20 Sample Frequency Response Function Data for Standard Test Plate .................. 34

3.21 Linearity Tests Results for Two Levels of Frame Acceleration .......................... 35

3.22 Repeatability Test Results for Standard Test Plate ............................................. 36

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4.1 Vibration Baseline Test Results for Undamped Plate ......................................... 38

4.2 Finite Element Model Results for Test Plate ...................................................... 39

4.3 Initial Mode Shape Identification....................................................................... 40

4.4 Standard Test Plate Response with Five Resonant Peaks Identified.................... 41

4.5 Laser Scanner Test Setup................................................................................... 41

4.6 Velocity Field for Peak 3 at 147 Hz from Laser Scanning Measurements........... 42

4.7 Acoustic Baseline Test Results for Undamped Plate .......................................... 43

4.8 Baseline Test Results Illustrating Vibration and Noise Correlation .................... 44

4.9 Velocity Field for Peak 2 at 121 Hz from Laser Scanning Measurements........... 45

4.10 PZT Placement on the Test Plate ....................................................................... 46

4.11 PZT Placement and Shunting Strategy............................................................... 47

4.12 Vacuum Procedure Setup................................................................................... 48

4.13 Smart Damping Plate Testing ............................................................................ 49

5.1 Test Plate Configurations Used to Evaluate the Benefits of Smart Damping ...... 51

5.2 Unshunted and Shunted Plate Vibration Response ............................................. 52

5.3 Effect of Adding Smart Material to an Undamped Plate..................................... 53

5.4 Third-Octave Band Analysis of Vibrations for Undamped and Shunted Plates... 54

5.5 Decrease in Undamped Plate Vibrations (Third-Octave Band)........................... 54

5.6 Effect of Smart Damping on Structure-Borne Noise of an Undamped Plate ...... 56

5.7 Noise Reductions Due to Smart Damping for an Undamped Plate ..................... 56

5.8 Third-Octave Band Analysis of Structure-Borne Noise for an Undamped Plate . 58

5.9 Decrease in Structure-Borne Noise for an Undamped Plate ............................... 58

5.10 Third-Octave Band Analysis for Undamped and Shunted Plates ........................ 59

5.11 Decrease in Acoustic Levels Using Smart Damping........................................... 60

5.12 Correlation of Plate Vibration Reductions to Structure-Borne Noise

Reductions……. ................................................................................................ 60

5.13 Passive Treatments Used with Smart Damping Materials................................... 61

5.14 Vibration Benefits of Smart Damping Materials for a Damped Plate.................. 63

5.15 Vibration Decrease Due to Smart Damping Materials Applied to a Damped

Plate…………................................................................................................... 64

5.16 Acoustic Benefits of Smart Damping Materials for a Damped Plate................... 66

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5.17 Decrease in NSPL Due to Smart Damping Materials Applied to a Damped

Plate…………................................................................................................... 67

5.18 Damping Treatments Applied to Test Plates ...................................................... 69

5.19 Different Foam Pads and Carpeting Damping Treatments................................. 69

5.20 Decrease in Accelerations with Respect to Added Weight ................................. 71

5.21 Decrease in Normalized Sound Pressure Levels with Respect to Added Weight 72

6.1 Floor Plan of Transmission Loss Test Facility.................................................... 74

6.2 Modified Test Window, Reverberation Room Side............................................ 75

6.3 Modified Test Window with Barrier Material for Calibration Test..................... 76

6.4 Undamped Plate with Smart Damping in Modified Test Window, Reception

Chamber Side .................................................................................................... 78

6.5 Plate Vibrations with Unshunted and Shunted PZTs .......................................... 79

6.6 Sound Pressure in Reception Chamber Before and After Turning on Shunt

Circuits.............................................................................................................. 80

6.7 Transmission Loss for Test Plate with Unshunted and Shunted PZTs ................ 80

6.8 Transmission Loss for Test Plate with Unshunted and Shunted PZTs ................ 81

6.9 Transmission Loss Results of Shunted and Unshunted PZT Plate with

Constrained Layer Damping .............................................................................. 82

6.10 Increased Transmission Loss Normalized with Respect to Added Weight.......... 83

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List of Tables

4.1 Experimentally-Determined Mode Shape Results .............................................. 43

5.1 Effect of Smart Damping on Peak Vibrations..................................................... 53

5.2 Normalized Noise Level Reductions Due to Applying Smart Damping to an

Undamped Plate ................................................................................................ 57

5.3 Different Treatments Tested with Smart Damping ............................................. 68

5.4 Weights of Different Treatments........................................................................ 70

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Chapter 1

Introduction

This chapter provides an introduction to the research that was conducted throughout the

course of this study. An introduction is given on noise, vibration, and harshness (NVH)

in vehicles and some of the current efforts for lowering NVH. Further, a summary of the

research objectives as well as an outline of the document are provided.

1.1 Introduction

In the past several years, there has been an increased marketplace awareness of noise,

vibration, and harshness performance in automobiles. The differentiation between the

quality and reliability levels of automobiles has become less pronounced and, as a result,

manufacturers have had to demonstrate superiority by focusing on NVH concerns. The

current battle began in 1989 when Toyota introduced its Lexus luxury line [1]. The

Lexus incorporated groundbreaking techniques for NVH improvements that resulted in

vehicles that were substantially quieter than any other car on the market. Lexus had set a

new standard for quality and increased customer expectations for both noise and vibration

comfort.

The automotive industry is currently spending millions of dollars on NVH work

to develop new materials and damping techniques. The new design methods are starting

to consider NVH issues throughout the whole design process, not just in the later stages.

This involves integrating extensive modeling, simulation, evaluation, and optimization

techniques into the design process to insure both noise and vibration comfort. New

materials and techniques are also being developed so that the damping treatments are

lighter, cheaper, and more effective. For example, the Lexus engineers had developed

unique metal panels where asphalt or other sound-insulating materials are layered

between two sheets of steel. They also used two-piece oil pans to help cut engine

booming, and liquid-filled engine mounts to isolate vibrations.

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Some of the current methods used to reduce noise and vibration in vehicles

originated in the 1920s. In 1927, Lord Corporation’s rubber-to-metal-bonded

components were used in General Electric trolley cars, and a few years later in Lincoln

and Nash automobiles [2]. Since then, many other methods and techniques have been

developed and implemented into vehicles of all kinds. Some of the methods used to

control noise, vibration, and harshness include the use of different carpeting treatments,

the addition of rubber or asphalt material to car panels, gap sealant, and the injection of

expandable foam into body panels. The carpeting treatments include varying types of

foam padding combined with different weights of rubber-backed carpet. The overall

result of this technique is a mass-spring system that acts as a vibration absorber. The

rubber or asphalt materials are attached to various car panels to add damping and mass

loading to reduce vibration levels and the rattling sounds from the panels. Sealant is

applied to close gaps in order to increase the transmission loss from the engine, wind, and

road noise sources to the vehicle interior. Expandable foam injected between panels,

such as the dashboard and firewall, helps to add stiffness and vibration absorption.

All of these current methods are effective at reducing sound and vibration levels

in a vehicle at higher frequencies. However, some of the treatments become almost

ineffective at lower frequencies below 200 Hz. The treatments also add a substantial

amount of weight to the vehicle, thus affecting its fuel economy, as well as adding cost.

1.2 Research Objectives

The primary purposes for this study were to:

1. Explore the feasibility of smart damping materials, such as piezoelectric

materials, for augmenting and improving the performance benefits of passive

damping materials, and

2. Provide a preliminary evaluation of the noise and vibration benefits, and

weight savings of smart damping material as compared to conventional

damping treatments.

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1.3 Approach

To achieve the objectives of the study, a special test rig was constructed and validated in

the early stages of the study. Upon validating the test rig and the instrumentation that

was set up for data collection and processing, a series of tests were performed. The tests

were intended to establish a baseline for the test rig and compare the performance of

smart damping materials with a number of passive interior automotive treatments.

Further, in order to evaluate the effect of smart damping materials on the sound

transmission loss, a series of tests were conducted at a standardized transmission loss test

facility, according to the SAE J1400 test specifications. The tests evaluate the

transmission loss for smart damping materials for an undamped and a damped plate.

1.4 Outline

Background information for this study, provided in Chapter 2, includes an explanation of

piezoceramic materials, possible applications of piezoceramics, and a literature review on

related research. This chapter also includes a detailed description of the shunt circuit

design and the methodology for PZT attachment.

Chapter 3 focuses on the test setup for the structural vibration tests. This chapter

includes justification and explanation of the test rig. Test rig construction and validation

tests are discussed as well as the test instrumentation.

Baseline testing for the test plate is described in Chapter 4. This chapter discusses

how the smart damping test plate was constructed. A finite element analysis is presented

and validated with laser vibrometer measurements, followed by the placement strategy of

the piezoceramic material.

The experimental results from the test rig are presented in Chapter 5. A summary

of the test results is used to evaluate the effectiveness of the smart damping.

Chapter 6 discusses the transmission loss tests performed and presents the test

results evaluating the effectiveness of smart damping techniques on increasing

transmission loss.

Finally, Chapter 7 summarizes the results of the study and provides

recommendations for future research.

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Chapter 2

Background

This chapter provides background information applicable to the objectives of this study.

First, piezoelectric materials are further defined with an explanation of the piezoelectric

theory and the possible applications of piezoelectric materials. Next, the literature search

conducted in the areas related to this research is discussed. Finally, the details of the

shunt design for this study are presented.

2.1 Piezoelectric Theory

Pieozoceramics are materials that demonstrate what is known as the piezoelectric effect:

Piezoelectric Effect; appearance of an electrical potential across somefaces of a crystal when it is under pressure, and of distortion when anelectrical field is applied. Pierre Curie and his brother Jacquesdiscovered the effect in 1880. It is explained by the displacement ofions, causing the electric polarization of the crystal’s structural units.When an electrical field is applied, the ions are displaced byelectrostatic forces, resulting in the mechanical deformation of thewhole crystal. Piezoelectric crystals are used in such devices as thetransducer, record-playing pickup elements, and the microphone.

-Encarta Concise Encyclopedia[3]

This effect occurs naturally in quartz crystals, but can be induced in other

materials, such as specially formulated ceramics consisting mainly of Lead, Zirconium,

and Titanium (PZT). Because they are ceramics (piezoceramics), they can be formed to

most any shape or size. In order to “activate” the piezo properties of the mix of metals,

the material is first heated to its Curie temperature. There, a voltage field of a sufficient

strength is applied in the desired direction, forcing the ions to realign along this “polling”

axis. When the ceramic cools, the ions “remember” this polling and act accordingly.

Much reference is made to piezo axes and their relation to the poling axis.

Convention and the IEEE Standard on Piezoelectricity [4] state that the poling axis be

termed the “3” direction with the same positive/negative sense as the applied voltage

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field. The remainder of the coordinate system is analogous to a right-handed orthogonal

system, mapping x-1, y-2, and z-3 , as shown in Figure 2.1 [5].

Figure 2.1. Basic Symbols and Terminology in Piezoelectricity

2.2 Applications for Piezoceramics

The piezoelectric effect provides the ability to use these materials as both a sensor and

actuator. Strain, for example, can be measured by capturing the voltage created across

the material when it is strained. As a sensor, these materials can also be used for damage

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detection in structures in which they are imbedded. Piezoceramics can be used as

actuators because they can strain or displace when an electric voltage is applied across

the poling axis. This makes PZTs good candidates for valve actuation or active control

systems. Piezoceramics are also used as structural dampers because of their ability to

efficiently transform mechanical energy to electrical energy and vice versa. When a

piezoelectric element, PZT, is used for passive vibration suppression, the force from the

vibration strains the PZT, which generates a voltage difference. This voltage, electrical

energy, can then be dissipated through a resistive circuit [6]. For example, the use of

piezoelectric elements for passive electronic damping has already been proven to work

effectively in commercial products such as the K2 ski. The K2 ski designers used a

resistor and capacitor (RC) shunt circuit to dissipate the vibration energy absorbed by

piezoelectric devices imbedded into the skis [7]. Active Control eXperts, Inc. developed

the Copperhead ACX bat that has shunted piezoceramic materials that convert the

mechanical vibration energy into electrical energy. This method of damping significantly

reduces the sting during impact and gives the bat a larger sweet spot [8].

2.3 Literature Search

A literature search was conducted to investigate past research related to the use of smart

materials to control structural vibration and noise. The specific areas that were

considered for the literature search included the utilization of smart materials for passive

damping, increasing transmission loss, and reducing vehicle vibration and noise, as

shown in Figure 2.2. Two databases, INSPEC and AppSciTechAb, were used for the

literature search. INSPEC is a leading database for physics, electronics, and engineering

research, and AppSciTechAb is another source for applied science and technology

literature.

The search was conducted using the keywords of the primary areas of interest,

which were “structural vibration” and “smart materials”, as shown in Figure 2.2. The

smart materials were searched as “PZT,” “piezoceramic,” and “piezoelectric” in order to

maximize the number of matching research topics. The literature search resulted in a

large number of articles in general areas such as “structural vibration” and damping with

smart materials. As such, all the works that were reviewed were taken from the results of

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the search areas highlighted in Figure 2.2. A summary of the search results is provided

next.

Figure 2.2. Literature Search Flowchart

2.3.1 Control of Structural Noise and Vibrations with Smart Materials

Structural controls have recently been used to reduce acoustic radiation from vibrating

structures, also referred to as structure-borne noise. Almost all of the studies have

involved the implementation of an active control system. Sun et al. used piezoelectric

actuators to reduce the structural vibrations and interior noise of a uniform cylindrical

shell that models a fuselage section [9]. Two distributed piezoelectric actuators were

developed based upon the understanding of structural-acoustic coupling properties of the

system.

Control of sound radiation from a plate in an acoustic cavity using smart materials

was investigated by Shields et al. [10]. They applied a patch of active piezoelectric

StructuralVibration

(323)

PZT (incl. Piezoceramic,

Piezoelectric)(28,085)

Vehicle Noiseand Structural

Vibration(43)

Damping w/PZTs(6634)

PZT & SoundTransmission

Loss (5)

Control ofStructural Noiseand Vibrations

w/PZTs(9)

PassiveDamping w/PZTs (97)

PZT ActiveDamping

(528)

Vehicle Noise andStructuralVibration

Damping w/ PZTs(2)

Passive Dampingw/PZT Shunt Circuits

(15)

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damping composites to the center of a 29.8-cm square plate made of thin aluminum. The

patch was made of PZT fibers embedded in resin. Using a derivative feedback controller,

they obtained a 70% attenuation of vibration and sound pressure levels. Active control of

sound radiating from a plate was also demonstrated by Varadan et al. on a thin square

metal plate [11]. The structural vibrations of the plate responsible for the sound/noise

radiation were actively controlled with piezoelectric sensors and actuators. This effective

method of active noise control was demonstrated for the interior noise of a cabin

enclosure by Varadan et al. [12]. They used discrete piezoelectric actuators and sensors

for the active vibration control of the walls of the enclosure. They were able to achieve

significant global noise reduction within the cavity for the dominant modes of the

radiation panel.

2.3.2 Vehicle Vibration and Noise Control Using Smart Materials

Lecce et al. demonstrated vibration active control in a vehicle by using piezoelectric

sensors and actuators [13]. The active structural acoustic control was developed by

integrating piezoceramic materials as sensors and actuators into some structural elements

of the car. By controlling the vibrations, the structure-borne noise was reduced. A

simple feed forward control system was implemented to control the floor panel

vibrations.

2.3.3 Increasing Transmission Loss with Piezoceramics

Active control using piezoceramics has been implemented to control the sound

transmission through a panel. Henrioulle et al. added a flexible honeycomb structure

with a piezoelectric PVDF (polyvinylidene fluoride) layer to a double panel partition

[14]. With active control of the PVDF, they were able to increase the transmission loss

by 10 dB at frequencies below 400 Hz. Xiaoqi et al. used active control with

piezoelectric actuators and sensors to increase the transmission loss through a thin

aluminum plate [15]. The plate was actively controlled at the resonance frequencies of

the passive plate where the isolation performance was poor. With one sensor and one

actuator, a global sound reduction of 15-22 dB was achieved at the first three resonance

frequencies.

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2.3.4 Passive Damping Using Shunted Piezoceramics

In addition to the K2 ski designers, many researchers have investigated the use of passive

electric shunts as a potential way to suppress vibrations. In 1979, Forward was the first

to suggest the possibility of using passive electrical shunts with piezoelectric elements for

vibration damping and control [16]. Forward experimentally investigated the effect of

using inductive shunting with a piezoelectric element on a metal beam. Hagood and von

Flotow developed the first quantitative analytical models for piezoelectrics shunted with

two types of circuits, a resistor circuit (RC) and a resistor and inductor circuit (RLC) [6].

They showed that when a PZT was attached to a resistor circuit, the frequency

dependence of the PZT was similar to visco-elastic damping materials. A PZT shunted

with the inductor and resistor had an electrical resonance that could be tuned to be similar

to a vibration absorber. Hagood and von Flotow validated both circuit models

experimentally on a cantilevered beam and developed techniques that analyzed shunted

systems. Further piezoelectric theory was developed by Davis and Lesieutre on the

damping performance prediction of shunted piezoceramics [17]. They developed a

method where the damping is predicted from the effective fraction of the modal strain

energy stored in the PZT, the effective piezoelectric material loss factor, and the

frequency shaping factor. They determined the strain energy factor using finite element

methods, the loss factor to be related to the electromechanical coupling coefficient, and

the frequency shaping factor from the dynamic response of the shunting circuit.

Since Hagood and von Flotow’s initial research, many have worked to

understand, optimize, and improve shunting techniques. Edberg et al., for instance,

replaced the heavy commercial inductor used by Hagood with a lightweight electronic

circuit [18]. They also showed that it was possible to simultaneously dissipate two

vibration modes using one tuned shunt circuit. Hollkamp also expanded the piezoelectric

theory to show that it was possible to suppress multiple modes using a single PZT [19].

However, due to mutual loading effects between multiple shunts, it was experimentally

difficult to simultaneously tune the shunts to different modes. Wu analyzed the

piezoelectric shunt theoretically using a PZT shunted with a parallel resistor and inductor

circuit for passive structural damping and vibration control [20]. This design, illustrated

in Figure 2.3a, proved easier to tune than the shunt design investigated by Hagood and

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10

von Flotow, shown in Figure 2.3b. The load resistor and inductor of the new shunt

design could be changed independently, and adjusting the load resistor had no effect on

the circuit resonance frequency. Wu used this modified shunt circuit design to develop a

method for damping multiple vibration modes using a single piezoelectric patch. They

employed “blocking” circuits that consisted of a parallel capacitor-inductor anti-resonant

circuit. This circuit was placed in series between shunt circuits designed for one

structural mode. These “blocking” circuits were designed to be open-circuited at all

frequencies except the resonant frequency to which their branch shunts circuit is tuned.

This method proved to be more reliable and easier to tune and optimize than method used

by Hollkamp. Wu demonstrated this method by suppressing the first two to three modes

of a two-wing cantilevered beam with a single PZT.

(a) Shunt Circuit Concept Used by Wu

(a) Shunt Circuit Concept Used by Hagood and von Flotow

Figure 2.3. Shunt Circuit Design Concepts Used by Hagood and Wu

Later, Wu and Bicos demonstrated multimode shunting on a composite plate

structure [21]. In addition to Wu and Bicos, the application of passive smart damping on

a plate has been researched by others as well. For example, Hollkamp and Gordon

compared the damping effectiveness of a piezoelectric vibration absorber with

constrained layer damping treatment on an electronic chassis box [22]. The results

showed that the piezoelectric absorber could provide vibration suppression comparable

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11

with that obtained with the constrained layer damping. Ghoneim investigated the

application of shunted piezoelectric damping on a cantilevered plate [23]. His

investigation was mainly analytical and qualitative with preliminary experimentation.

Ghoneim argued that the shunted piezoelectrics were more effective at suppressing

resonant vibration amplitudes with a wider effective range of vibration control than

constrained layer damping.

Passive piezoelectric damping has also been applied to space structures in

research conducted by Aldrich et al. [24], and Edberg and Bicos [25]. Aldrich et al.

implemented 0.5 kg of piezoelectric material to damp a 5000-kg structure. Their study

included active and passive damping using piezoelectric materials. Resistive

piezoelectric shunting provided the necessary broadband damping. Edberg and Bicos

investigated implementing shunted piezoelectric materials in structural struts that may be

installed in a truss structure.

Another aspect of shunted piezoelectric damping that has been researched is the

methodology of tuning the shunt circuit for optimal response. Piezoelectric materials

shunted with resonant circuits are designed to minimize structural vibrations at a specific

frequency. This frequency, however, may shift in practical applications thus reducing the

effectiveness of the tuned vibration absorber. As such, researchers such as Hollkamp and

Starchville [26], and Davis and Lesieutre [27] have investigated implementing active

self-tuning circuits. Hollkamp and Starchville used a cantilevered beam mounted with

PZTs attached to resonant shunt circuits to demonstrate active tuning. The PZT vibration

absorbers were designed to tune themselves to a particular mode and track the mode as it

varies in frequency. The control system achieved this by comparing the structural

response of the beam to the shunt circuit response. Davis and Lesieutre demonstrated

active tuning for a piezoelectric vibration absorber with a passive capacitor shunt circuit.

They developed a control scheme that estimated the desired tuning frequency from

sensors and determined the appropriate shunt capacitance. The shunt circuit was tuned

using a relay-driven parallel capacitance ladder circuit designed to tune the shunt in ten

discrete steps over the tuning range. With their actively tuned shunt design, Davis and

Lesieutre were able to achieve a 10 dB improvement in vibration reduction over passive

resonant shunt damping.

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2.4 Shunt Circuit Design

The smart damping technique chosen for this study involved attaching piezoceramic

devices that are shunted with passive electrical circuits. When the panel vibrates, as

illustrated in Figure 2.4(b), the mechanical energy strains the piezoelectric material and

thereby generates electrical energy (i.e. voltage). The shunted electrical impedance then

dissipates this electrical energy. The components of these shunt circuits (resistors,

capacitors, and inductors) are chosen to produce an effective mechanical impedance at

desired levels and frequencies.

(a) Network Analog of Shunt Model

(b) Simple Physical Model of a Uni-Axial Shunted PZT

Figure 2.4. Shunting of Piezoelectric Materials

As shown in Figure 2.4(a), the shunt circuit that was chosen for this application

was an RLC circuit, similar to the one demonstrated by Hagood and von Flotow [6].

Although there have been many improvements made on this shunting concept, this shunt

was chosen because it was the established design implemented at the Center for

T- Stress by Plate on PZT Vi- PZT VoltageI- Circuit Current Rs- Shunt ResistanceLs- Shunt Inductance Zs-Equivalent Shunt ImpedanceZm-Plate Mechanical Impedance Cpi-Inherent PZT Capacitance

Electrical Resonant Frequency:

ωe=1/ LsCpi

Ref. H.W. Hagood, and A von Flotow, “ Damping of Structural Vibrations with Piezoelectric Materialsand Passive Electrical Networks,” Journal of Sound and Vibration, Vol. 146, No.2, pp. 243-268, 1991

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Intelligent Material Systems and Structures Lab at Virginia Tech. Future studies in this

area may select other shunt circuits that are more suitable for their intended applications.

The basic resonant shunt design consists of a resistor, an inductor, and a capacitor.

The resistor in the circuit is referred to as the load resistor because it is the mechanism

that dissipates the electrical energy. This resistor value ranges from 0 to 14,000 Ω, and

dissipates around 0.002 W of energy from the plate at resonant peaks. The electrical

resonance of the circuit is determined by the value of the inductance and the capacitance,

as in Equation (2.1).

LsCpie

1=ω (2.1)

The capacitor, Cpi, for the circuit is the PZT itself because electrically, it behaves similar

to a capacitor. The capacitance value of the circuit cannot be changed in order to tune the

circuit at a desired resonant frequency unless a variable capacitor is added in parallel or

series. If the capacitance of the PZT has to be reduced, a variable capacitor can be added

in series with the PZT. Alternatively, a variable capacitor can be added in parallel with

the PZT to increase the capacitance. Another simpler alternative is to use a variable

inductor as the shunt inductor in order to tune the circuit. The inductance for the RLC

circuit, Ls, was simulated with an operational amplifier circuit as shown in Figure 2.5

[28].

Figure 2.5. Operational Amplifier Circuit Emulating a Variable Inductance

The resistor, R2, is a variable resistor that can be adjusted in order to change the circuit

inductance. The components labeled R1, R3, and R4 are 10kΩ resistors, and C1 is a

10,000µF capacitor. The details of one of the experimental shunt circuits are pictured in

Figure 2.6, where RL is the load resistor. The leads from the positive and ground poles of

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the PZT are inserted at the marked nodes. The operational amplifier uses a ±15 Volts

power source, but requires less than 1 Watt of power to run. This shunt-power supply

configuration is illustrated in Figure 2.7.

RL R2

R4 R3 R1

C1

OpAmp

-15V +15V GND

PZT +PZT GND

Figure 2.6. Experimental Shunt Circuit Board (Single Shunt)

±15 V Power Supply(for OpAmp)

Shunt CircuitPZT +

PZT GND

Figure 2.7. Single Shunt Circuit and Power Supply Configuration

2.4.1 Shunt Tuning

The purpose of this section is to describe the methods used for tuning the PZT resonant

shunt circuits. The first step is to determine the electrical resonant frequencies required

to dissipate the mechanical energy. The second step is to calculate the initial values for

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the variable resistors in the shunt circuit. The final step is to fine-tune the resistors with

testing in order to achieve optimal damping.

An optimal electrical resonant frequency must be calculated because the electrical

resonant frequency is not exactly the same as the resonant plate frequency due to inherent

damping in the plate and added damping of the shunt circuit. An optimal tuning ratio,

δopt , is calculated to determine the electrical resonant frequency of the circuit, ωe. Several

experimental parameters must be determined beforeδopt and ωe can be calculated. These

parameters include the natural frequencies of the plate when the PZT is open- and short-

circuited; the generalized electromechanical coupling coefficient, K31; optimal tuning

inductance and capacitance; and the shunting resistance for each mode. It is difficult to

determine these optimal tuning parameters using the conventional shunt circuit theories

developed by many researchers for two main reasons. The first is that the PZT

capacitance and the shunt inductance have some internal resistances and these are not

negligible. The second is that the material parameters of capacitors (PZTs) used in the

shunt electric circuit vary 5-10 % from manufacturer’s values.

First, the capacitance of the PZT should be determined roughly (since capacitance

is dependent on frequency) using Equation (2.2):

CK A

tpT

Tp

p

=× ×3 0ε

(2.2)

where TpC is the capacitance of the PZT at constant stress, KT

3 is the relative dielectric

constant at 1KHz, the constant εo is 885 1012. × − F/m, Ap is the surface area of PZT, and tp

is the thickness of the PZT. These values were provided by the manufacturer, Piezo

Systems, Inc. The product of K T3 0ε is called the permittivity of the dielectric denoted ε.

The PZT capacitance at constant strain, CpS , is obtained from Equation (2.3):

( )C C kpS

pT= −1 31

2 (2.3)

which is dependent upon the electromechanical coupling coefficient, k31, provided by the

manufacturer.

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Second, the generalized electromechanical coupling constant for a piezoelectric

bonded to a structure can be obtained from the frequency change of the electric boundary

conditions [5]:

( ) ( )( )

KnD

nE

nE31

2

2 2

2=−ω ω

ω (2.4)

Here, ωnD and ωn

E are the natural frequencies of the structural mode of interest with an

open circuit piezoelectric and a short circuit piezoelectric, respectively. These

frequencies can be obtained from the frequency response function. The other optimum

tuning parameters are calculated from the values determined above as follows:

δopt K= +1 312

and mopte ωδω = (2.5)

where δopt is the optimal tuning ratio, and ωe is the electrical resonant frequency.

The shunt inductance and PZT capacitance determine the electrical resonance of the

circuit as in the equation:

Sps

eCL

1=ω (2.6)

The shunt inductance, Ls, as illustrated in Figure 2.4b, is calculated from ωe and the PZT

capacitance, SpC :

Spe

s CL

2

1

ω= (2.7)

The equivalent inductance of the op-amp circuit shown in Figure 2.5 is determined to be

1*CRLeq = (2.8)

where

2

431*

R

RRRR =

(2.9)The resistor, R2, in the inductor circuit shown in Figure 2.5 is a variable resistor that is

adjusted in order to change the circuit inductance.

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For a desired inductance of Ls, the value of R2 is determined from the equation:

sL

CRRRR 1431

2 = (2.10)

To determine the optimal shunt load resistance, RL of Figure 2.5, the optimal damping

ratio, ropt, must be calculated using the value K31 from Equation (2.4):

rK

Kopt =+

21

31

312 (2.11)

The optimal shunt load resistance, Ropt, is then calculated as

Rr

Copt

opt

pS

nE

=ω (2.12)

The values for the inductor resistance and load resistance were calculated using the m-file

included in Appendix A. These values were used for the initial tuning of the shunt

circuit; fine-tuning was then performed during testing, as described in Appendix B.

2.5 Summary

This chapter presented background information on piezoelectric materials, including an

introduction to the piezoelectric effect and possible application of piezoelectric materials.

A literature review was included to present research topics related to this study and to

provide additional background information on piezoelectric materials. Finally, the shunt

circuit design used for this study was explained in detail.

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Chapter 3

Experimental Setup

This chapter describes the experimental setup of the test stand used for laboratory testing

at the Advanced Vehicle Dynamics Lab (AVDL) of Virginia Tech. First, the structural

design of the test stand will be discussed. Next, the test setup will be described including

the input excitation and data acquisition systems. Tests that validate the frequency range,

linearity, and repeatability of the test stand will also be presented.

3.1 Test Stand Design

The test stand was designed and fabricated for testing and evaluating the effectiveness of

piezoelectric damping materials for reducing both vibrations and structure-borne noise.

The test stand enables vibration and acoustic measurements and analysis on a steel plate

with clamped-clamped boundary conditions. The plate, simulating an automotive

structure, is clamped rigidly around its edges and excited over a frequency range of 50-

450 Hz. Various standard flooring materials, such as carpeting, passive damping

materials, and smart damping materials, are added to the panel in order to evaluate their

effect on reducing the plate vibrations and subsequent noise.

The test stand, shown in Figure 3.1, includes a bottom enclosure, top enclosure,

excitation frame, and electromechanical shaker. Measurements are taken with two

accelerometers, located on the plate and excitation frame, and a microphone positioned in

the upper reception chamber. The reception chamber and bottom enclosure are designed

to eliminate background noise and isolate the noise generated by the electromagnetic

shaker and the plate.

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The first part of the test stand is a four-sided box that rests on the ground and

encloses the shaker and excitation frame, as shown in Figure 3.1. The excitation frame

attaches to the shaker with a stinger rod, and hangs from the box by four springs. The

test plate rests on top of the excitation frame and is bolted in place by a clamping frame

structure resembling a picture frame. Another component of the test rig is the top

enclosure, a five-sided box that rests on top of the bottom box. A microphone hangs

from the top of this enclosure, at a distance of 500 mm above the center of the test plate.

The microphone is used to measure the noise emitted by the test plate during frame

excitation. The following sections describe the design details of various components of

the test stand.

3.1.1 Bottom Box Enclosure

The bottom box framework, illustrated in Figure 3.2, is constructed from high strength

extruded aluminum beams manufactured by 80/20 Inc. The aluminum beams have

extruded T-shaped profiles that allow nuts to be captured, thus facilitating easy joining

and bracing of the structure. As shown, the box frame is supported at the corners by

aluminum gussets which are also manufactured by 80/20 Inc. The bottom box width and

depth were designed to fit the excitation frame dimensions. The height was designed so

Figure 3.1. Vibration and Acoustics Test Stand Schematics

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that the box could accommodate the shaker, the stinger, and the excitation frame. This

yielded a box 38 in high, 40 in wide, and 36 in deep. The excitation frame hangs from the

bottom box framework.

The back, left, and right sides of the box are made from 20-gauge steel sheet. The

inside faces are covered with viscoelastic barrier material to help isolate the structure

from vibrations, and to act as a gasket between the 20-gauge sheet and the aluminum

beams.

38”

36”

40”

Figure 3.2. Frame for Bottom Box Enclosure

The inside of the enclosure is lined with acoustical foam to absorb the acoustical energy

emitted by the bottom of the test plate, minimizing any reflected sounds. This is

necessary because the sound level measured by the microphone must come from one

source, the test plate. The acoustical foam is attached to Styrofoam frames that are glued

to the inside of the steel sheets. These Styrofoam frames allow air between the acoustical

foam and the steel sheet, providing further acoustical insulation. Figure 3.3 shows a

sectional view of one side of the bottom enclosure, looking down from the top. The front

side of the enclosure is similar to the other sides, except that it is made from 1/8-inch-

thick steel sheet because it must accommodate the front door.

To isolate the enclosure from vibrations transmitted through the floor by the

shaker, closed-cell foam is placed between the bottom of the bottom box and the floor.

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Closed-cell foam is also placed on the top/bottom box interface so that the top box rests

on the closed-cell foam and not directly on the bottom box. This helps to better

acoustically seal the top and bottom boxes.

air

acoustical foam

viscoelasticbarrier material

Styrofoam

20 ga. steel sheet

Figure 3.3. Section View of Bottom Box Enclosure Side

A 26 in x 26 in 20 gauge steel door, shown in Figure 3.4, seals a 2 ft x 2 ft opening in the

bottom enclosure that allows access to the shaker and excitation frame. Magnetic gasket

material, similar to a refrigerator door, was attached to a two-inch overhang on the door

in order to seal the door acoustically. Viscoelastic barrier material, Styrofoam, and

acoustic foam were applied to the door in the same manner as to the other sides of the

box. The door has two handles and is supported by two hexagonal bolts attached to the

1/8-in sheet below the door.

handles

door

steelsheet

Figure 3.4. Front Side of Bottom Box Enclosure with Door

SupportBolts

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3.1.2. Top Box Enclosure

The top box was designed to be similar to the bottom box, incorporating the extruded

aluminum beams and 20-gauge steel sheets for the top, front, back, right, and left sides.

The sides were bolted to the beams and had damping and acoustical foam installed in the

same manner as in the bottom box. The overall dimensions of the top box are 40 in high,

40 in wide, and 36 in deep. The top enclosure, however, did not need to support

structural loads, so smaller beams were used in the frame. The inside face of the top

panel has 8-inch acoustic wedges glued to a foam sheet instead of the acoustical foam.

Figure 3.5 shows the inside of the top box, looking up into it towards the top (the 8-in

acoustic wedges are white). Four handles are mounted to the top of the reception

chamber so that a chain and a hoist can be attached in order to raise and lower the

enclosure.

Figure 3.5. Inside of Reception Chamber

3.1.3. Excitation Frame

The excitation frame, shown in Figure 3.6, is an inverted trapezoidal pyramid that is 50

cm in height and has bases that are 15 cm x 15 cm and 50 cm x 60 cm in dimension. The

frame was designed so that none of its flexural modes would occur in the range of

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23

frequencies to be measured. If a natural frequency of the frame would occur between 50

and 450 Hz, then it would distort the excitation energy from the shaker to the test plate.

This in turn distorts the output data, resulting in poor coherence measurements between

the input and output signals.

arm

Figure 3.6. Excitation Frame

Four horizontal arms welded to the frame, as shown in Figure 3.6, are used to

suspend the excitation frame from the frame’s upper beams. As shown in Figure 3.7,

each arm has a suspension configuration that is an extension spring with an eyebolt

attached at its ends. One eyebolt connects to the frame arm, and the other eyebolt

connects to the bracket that mounts to the enclosure frame. The springs allow the

excitation frame to oscillate vertically, transmitting the vibrations to the test plate. The

springs were designed such that the suspended frame dynamics do not interfere with the

test plate dynamics. The rigid body modes of the suspended frame were determined to be

below 10 Hz, and therefore below the test frequency range of 50-450 Hz.

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excitationframe

acousticalfoam

arm

bracket

spring/boltsbox framebeam

Figure 3.7. Excitation Frame Mount to Bottom Box

The clamping frame is bolted to the excitation frame so that the test plate is clamped

securely between the frames, as shown in Figure 3.8. The frame was fabricated from 2-in

steel angle iron steel with a 1/8-in thickness. The outside dimensions of the frame are the

same as the test plate, which is 600mm x 500mm. The inside dimensions of the frame

are 500mm x 400mm.

test plate

clamping frame

Figure 3.8. Clamping Frame on Excitation Frame

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3.1.4 Electromagnetic Shaker

The electromagnetic shaker, shown in Figure 3.9, is a VTS g100-6 100-lb shaker that is

bolted to a heavy steel stand that rests on the floor. An amplifier located outside of the

enclosure powers the shaker. A stinger rod screws into the top of the shaker at one end

and is bolted to the bottom of the excitation frame at the other end.

Excitation Frame

Shaker

Stinger Rod

Figure 3.9. Electromagnetic Shaker and Stinger Rod Assembly

3.1.5 Total Test Stand Assembly

As mentioned in Section 3.1.2, a hoist is used to lift and lower the top enclosure on and

off the bottom enclosure. The full test stand assembly, shown in Figure 3.10, includes a

wooden cart, painted white, that was constructed as a stand for the top enclosure. The top

enclosure, which rests on this cart, can be wheeled away from the bottom enclosure in

order to access the excitation frame. To lower the enclosure for testing, the cart is

wheeled over the bottom and the chain is hooked into the hoist located above the stand.

The top enclosure is lifted off the cart, the cart is wheeled out of the way, and the top

enclosure is then lowered onto the bottom enclosure.

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Figure 3.10. Total Test Stand Assembly

3.2 Test Setup

This section outlines the test plate set up, the transducer arrangement, and the data

acquisition system used for the structure-borne vibration and noise testing.

3.2.1 Test Plate Setup

For testing, a standard test plate was clamped into place with 14 bolts tightened to a

torque of 25 N-m. The standard plate was a 500mm X 600mm, 20-gauge, galvanized

steel plate. The plate was bolted as in Figure 3.11 such that the outside 10 cm along the

edges were clamped and the remaining test plate area was 400mm X 500mm. The bolts

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27

were always tightened in the same criss-crossing pattern, similar to that for lug nuts on a

car wheel, to improve the repeatability of the boundary conditions for the plate.

600 mm

500 mm

500 mm400 mm

Effective Test Plate Area

Figure 3.11 Standard Test Plate in Testing Position

An acoustic barrier was then placed over the top of the frame and bottom

enclosure, illustrated in Figure 3.12, so that only the test plate area was exposed to the

reception chamber.

Effective TestPlate Area

Acoustic Barrier (Entire White Area)

Figure 3.12. Acoustic Barrier Arrangement

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28

3.2.2 Transducer Arrangement

Accelerometers and a microphone were used to measure the frame acceleration, the plate

acceleration, and the structure-borne noise. Two PCB Model 33A accelerometers were

used to measure the input acceleration of the excitation frame and the plate response

acceleration, as shown in Figure 3.1. For the excitation frame, an accelerometer was

attached underneath the center of the front top beam. The frame acceleration, assumed to

be only in the vertical direction, measures the input for the plate vibration and structure-

borne noise. The other accelerometer was attached underneath the center of the test plate

to measure the vibration response of the plate. A B&K ½-in microphone (Falcon Range

Type BP 1422) was positioned, as shown in Figure 3.13, in the reception chamber such

that it was 0.5 m above the center of the test plate during testing. The microphone was

secured to a ½-in threaded steel rod that bolts to the top of the reception chamber.

threaded rod

microphone

Figure 3.13. Microphone Placement in the Reception Chamber

3.2.3 Data Acquisition System

The data acquisition was set up according to the test schematic shown in Figure 3.14.

The Hewlett Packard dynamic signal analyzer served as the data recorder, the fast Fourier

transformer, the band pass filter, and the signal generator for controlling the shaker.

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29

Figure 3.14. Shaker Table Test Stand and Data Acquisition Schematic

Initial tests and experiments were performed with a number of different excitation

functions and sampling techniques. A final sampling technique was chosen such that

coherence was the highest between the plate acceleration and frame acceleration, and test

chamber acoustics (microphone output) and frame acceleration. Coherence is derived

from the cross correlation between the input and output measurements. This sampling

technique uses the following:

• periodic chirp input signal,• uniform sampling window (0% overlap),• source triggering,• anti-aliasing filter,• 800 spectral lines, and• 20 averages.

A periodic chirp input signal, shown in Figure 3.15, was chosen because it had a uniform

distribution of energy across the frequency range.

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0 200 400 600 800 1000 1200 1400 16006

7

8

9

10

11

12x 10

-3 Linear Spectral Density of Generated Signal

Vo

lts/H

z

F requency, (Hz)

Figure 3.15. Periodic Chirp Signal Generated by HP Analyzer

3.3 Validation Tests

The goals of the validation tests were to ensure that there were no frame resonance

frequencies below 500 Hz, and that the parasitic noise, any noise emitted other than from

the test plate, was minimal. In addition to these goals, the tests were intended to verify

dynamic linearity and test repeatability of the test stand. For these tests, the coherence

was monitored to further validate the measurements.

3.3.1 Vibration Response Validation

Although the generated input signal is an ideal signal for testing the frequency response

for a plate, the direct input excitation for the plate is from the frame, not from the HP

analyzer. Therefore, the frame acceleration was chosen as the input signal for the plate

and sound pressure measurements. The desired excitation range for the plate is between

50 and 450 Hz; poor data will result if there are any resonant frequencies of the frame

within this range. The frequency response of the frame was then analyzed to ensure that

this was not the case. Data were first collected for the excitation frame and clamping

frame without the plate in place. Figure 3.16 clearly shows that the major frame

structural resonant frequencies occur above 500 Hz. The three rigid body modes, bounce,

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31

pitch, and roll, occur between 5 and 10 Hz. The acceleration frequency spectrum of the

frame within the 50-450 Hz range is relatively constant as well.

0 200 400 600 800 1000 1200 1400 160010

-4

10-3

10-2

10-1

100

Linear S pec tral Density of F ram e Output S ignal

Ac

ce

lera

tio

n,

gs

/Hz

F requenc y, (Hz )

Figure 3.16. Frame Acceleration Response without Test Plate Installed

Figure 3.17 shows the effect of the test plate on the frame response when it is

clamped in the frame. For the same amount of input energy to the shaker, the frame

acceleration is decreased due to mass loading from the plate. For this reason, the data are

always recorded relative to frame acceleration because different damping treatments will

have different mass loading effects.

There are also some coupling effects between the frame and plate at the resonant

frequencies of the plate. This is another reason for recording data relative to frame

acceleration. These resonant peaks are clearly illustrated in the sample data shown in

Figure 3.18 for an undamped standard test plate.

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32

50 100 150 200 250 300 350 400 450

10-3

10-2

Linear Spectral Density of Frame Output Signal

Acc

ele

ratio

n,

gs/

Hz

Frequency, (Hz)

Without PlateWith Plate

Figure 3.17. Effect of Test Plate on Frame Acceleration Response

50 100 150 200 250 300 350 400 45010

-2

10-1

100

101

102

Frequency Response Function, Plate Accleration/Frame Acceleration

Acc

eler

atio

n, g

s/gs

Frequency, (Hz)

50 100 150 200 250 300 350 400 450-200

-100

0

100

200

Pha

se, d

egr

ee

s

Frequency, (Hz)

50 100 150 200 250 300 350 400 4500.7

0.8

0.9

1

Coh

eren

ce

Frequency, (Hz)

Figure 3.18. Sample Frequency Response Function Data for Standard Test Plate

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33

3.3.2 Acoustic Response Validation

Acoustic validation tests were performed to determine the noise floor as well as to

measure how well the acoustic data correspond to the plate vibration data. Acoustic data

were also taken without the test plate to determine how much noise the frame and shaker

generated. It is clear from the data, shown in Figure 3.19, that the frame and shaker do

contribute some amount of additional noise, but the sound levels at the peak resonant

frequencies are at least 20 dB above the noise levels. Additionally, when the plate is in

place, the plate acts as an additional acoustics barrier. Sample acoustics data in Figure

3.20 show that there is a direct correspondence between plate accelerations and sound

pressure levels.

50 100 150 200 250 300 350 400 450-10

0

10

20

30

40

50

60

70Sound Pressure Levels With and Without Plate

SP

L, d

B

Frequency, (Hz)

With Plate Without PlateBackground

Figure 3.19. Sample Sound Pressure Levels With and Without Plate

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34

50 100 150 200 250 300 350 400 45010

-2

10-1

100

101

Frequency Response Function, Sound Pressure/Frame Acceleration

Pre

ssur

e/F

ram

e A

ccel

, Pa/

gs

Frequency, (Hz)

50 100 150 200 250 300 350 400 450-200

-100

0

100

200

Pha

se, d

egre

es

Frequency, (Hz)

50 100 150 200 250 300 350 400 4500

0.2

0.4

0.6

0.8

1

Coh

eren

ce

Frequency, (Hz)

Figure 3.20. Sample Frequency Response Function Data for Standard Test Plate

3.3.3 Repeatability and Linearity

Additional tests were performed to verify the linearity and repeatability of the tests

performed on the test stand. Linearity implies that if the frame acceleration is increased

by a certain ratio, then the plate acceleration and sound pressure will increase by the same

ratio. This effect results in frequency response functions that remain constant regardless

of the input level. As Figure 3.21 shows, relatively linear responses were achieved for

the sound pressure levels and the test plate accelerations due to the increased input level

(frame acceleration) within the 50 to 450 Hz frequency range.

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35

Ave Frame Accel= 1.6e-3 gAve Frame Accel= 1.0e-3 g

50 100 150 200 250 300 350 400 45010

-2

10-1

100

101

102

Frequency, Hz

Pla

te A

ccel

/Fra

me

Acc

el, g

s/gs

50 100 150 200 250 300 350 400 45010

-2

10-1

100

101

102

Linearity, Frequency Response Functions

Frequency, Hz

Pre

ssur

e/F

ram

e A

ccel

, Pa/

gs

Figure 3.21. Linearity Test Results for Two Levels of Frame Acceleration

Repeatability was also tested to verify that the clamping conditions remained

relatively constant from one test to the next, and that the natural frequencies and vibration

levels did not differ excessively. As illustrated in Figure 3.22, the test chamber sound

pressures and plate accelerations were quite similar for two tests conducted at different

times on a standard test plate. After Test 1 was completed, the plate and accelerometers

were removed. For Test 2, the plate was remounted in the test stand and the

accelerometers were reattached. In this regard, it was determined that as long as the test

setup guidelines are followed, as per Section 3.2, the tests were accurately repeatable.

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36

Test 1Test 2

50 100 150 200 250 300 350 400 45010

-2

10-1

100

101

102

Repeatabilty,Frequency Response Functions

Frequency, Hz

Pre

ssur

e/F

ram

e A

ccel

, Pa/

gs

50 100 150 200 250 300 350 400 45010

-2

10-1

100

101

102

Frequency, Hz

Pla

te A

ccel

/Fra

me

Acc

el, g

s/gs

Figure 3.22. Repeatability Test Results for Standard Test Plate

3.4 Summary

The test stand construction, the experimental setup, and the validation tests were

discussed in this chapter. The test stand was designed and built to perform structure-

borne vibration and noise experiments for the investigation of the application of smart

damping. The validation tests established the best excitation and sampling technique,

determined that there were no frame resonance frequencies below 500 Hz, and

determined that the parasitic noise was minimal. In addition, the validation tests verified

the dynamic linearity and test repeatability of the test stand.

Repeatability, Frequency Response Functions

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37

Chapter 4

Baseline Tests and Smart Plate Development

The purposes of this chapter are to discuss the baseline tests performed on the undamped

test plate and to outline the process used in developing the smart damping test plate. This

chapter describes the methods used to establish the vibration and acoustic characteristics

of the undamped plate, which in turn enabled the PZT material application to the

undamped plate for the smart damping plate development.

4.1 Baseline Tests

Baseline tests were performed on the undamped test plate according to the test setup

described in Chapter 3. Frequency response data were collected for the frame

acceleration, plate acceleration, and generated sound pressure levels. The results of the

baseline tests helped to establish the vibration and acoustic characteristics of the

undamped plate. Resonant peak levels and frequencies were selected from these baseline

tests, which were later further analyzed in order to determine the mode shapes, or

vibration patterns, of the plate. This information was used to determine the placement for

the smart material.

4.2 Test Plate Vibration Characteristics

This section investigates the vibration characteristics of the undamped test plate with

clamped-clamped boundary conditions. The corresponding mode shapes, the shapes in

which the plate vibrates, were identified in order to determine which modes would be the

most successfully decreased using smart materials. Mode shape identification provides

useful information for the placement of smart material. Baseline tests were performed

and then compared to a finite element analysis model. The mode shapes were then

verified using laser-scanning techniques that measure the velocity fields associated with

the resonance frequencies.

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38

4.2.1 Test Plate Resonance Frequencies

Baseline tests were performed for an undamped test plate, as described in Chapter 3, for a

frequency range of 0 to 400 Hz. Data from the plate and frame accelerometers were

collected and recorded using the HP analyzer according to the sampling technique

described in Section 3.2.3. Figure 4.1 illustrates the frequency response of the plate

vibration levels with respect to the frame acceleration. Distinctive resonant peaks can be

identified, with the highest levels occurring at 43 Hz, 106 Hz, 145 Hz, and 252 Hz.

0 50 100 150 200 250 300 350 400-20

-10

0

10

20

30

Frequency Response of Plate to Frame Accleration

Frequency, Hz

Mag

nitu

de,

Dec

ibel

s

45 Hz 106 Hz 145 Hz 252 Hz

Figure 4.1. Vibration Baseline Test Results for Undamped Plate

4.2.2 Test Plate Mode Shapes

The mode shapes of the resonant frequencies of the undamped plate were determined

using analytical as well as experimental methods. First, a finite element analysis was

performed and used to approximate resonant frequencies and the mode shapes.

Experimental tests were then performed on the plate using a laser vibrometer to measure

the velocity fields at the resonant peaks with the highest response levels.

4.2.2.1 Analytical Mode Shapes

An analytical analysis was performed using a 500-element model of a plate with 1.0 mm

thickness, an effective test plate area of 40 cm x 50 cm, and fixed boundary conditions.

Figure 4.2 presents the first twelve mode indices and natural frequencies that were

Frequency Response of Plate to Frame Acceleration

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39

obtained with Algor, a finite element package. For the mode index, (i, j), i and j are the

number of half-sine waves of vibration along the width and length of the plate,

respectively. These results were used to interpret the frequency response functions

generated in the baseline vibration tests for the undamped plate.

(1,1) Mode – 46.3 Hz (1,2) Mode – 81.4 Hz (2,1) Mode – 106.1 Hz

(1,3) Mode – 138.4 Hz (2,2) Mode – 138.8 Hz (2,3) Mode – 194.5 Hz

(3,1) Mode – 197.4 Hz (1,4) Mode – 215.8 Hz (3,2) Mode – 229.4 Hz

(2,4) Mode – 270.8 Hz (3,3) Mode – 283.1 Hz (1,5) Mode – 313.1 Hz

Figure 4.2. Finite Element Model Results for Test Plate

Vibration peaks of the baseline tests in Figure 4.3 have been labeled with a mode

index that was approximated using the finite element results. This was done with the

assumption that all the modes in the frequency range were measured, and the mode

shapes occurred in the same ascending frequency order. The finite element analysis

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40

produced similar but not exact results due to undeterminable factors such as damping

effects of the boundary conditions. This discrepancy for the boundary conditions causes

some uncertainty for the mode shape approximations shown in Figure 4.3. For this

reason, it was decided that the mode shapes of the plate had to be identified via

experimental testing and analysis. Laser scanning techniques were utilized due to their

speed, high resolution, and availability to the lab.

0 50 100 150 200 250 300 350 400-20

-10

0

10

20

30

Frequency Response of Plate to Frame Accleration

Frequency, Hz

Mag

nitu

de,

Dec

ibel

s

(1,1)

(1,2)

(2,1)

(1,3)

(2,2)

(2,3)

(3,1)

(4,1)

(3,2)

(2,4)

(3,3)

(1,5)

Figure 4.3. Initial Mode Shape Identification

4.2.2.2 Experimental Mode Shapes

Before laser measurements were performed, the baseline tests were retaken for the

frequency range of interest, 50-450 Hz. From the frequency response functions shown in

Figure 4.4, five resonant frequencies were selected as possible modes to dampen with

PZTs. Peaks 1, 2, 3, and 5 were selected because they had the highest accelerations.

Peak 4 was selected because later it was proved that it was possible to dampen both peaks

4 and 5 with one PZT and shunt circuit. These peaks are close together in frequency, i.e.

coupled, which makes it possible to tune the shunt circuit to a frequency between the two

peaks. Peaks 1 and 3 are well separated and therefore require different PZTs and shunt

circuits.

Frequency Response of Plate to Frame Acceleration

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41

50 100 150 200 250 300 350 400 45010

-2

10-1

100

101

102

Undamped Plate Frequency Response Function

Frequency, Hz

Pla

te A

ccel

/Fra

me

Acc

el,

gs/g

s1

23

4

5

Figure 4.4. Standard Test Plate Response with Five Resonant Peaks Identified

Laser scanning tests were performed on these selected peaks so that the shapes could be

determined. For this test, the top enclosure is removed and a laser is suspended over the

test plate, as shown in Figure 4.5. While the plate is excited at the desired frequencies,

the laser scans the plate and records the plate velocity field.

Laser

Scanned Area

Figure 4.5. Laser Scanner Test Setup

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42

Velocity fields were determined for the five selected peaks at 101, 121, 147, 235, and 245

Hz. Figure 4.6 shows the experimental results for peak 3 at 47 Hz. It is evident here that

this mode index is (3,1), which was predicted correctly with the finite element analysis.

Figure 4.6. Velocity Field for Peak 3 at 147 Hz From Laser Scanning Measurements

The experimentally-determined mode indices for the five resonant peaks are listed in

Table 4.1. The mode shapes of peaks 1, 3, 4, and 5 are considered odd mode shapes

Magnitude of Plate Velocity at 147 Hz, Mode (3,1)

Magnitude of Plate Velocity at 147 Hz, Mode (3,1)

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43

because both the i and j indices are an odd number. Peak 2 has an even mode shape,

(2,2), because its indices are even. The significance of even or odd mode shapes is

addressed in the next section, where the test plate acoustic characteristics are

investigated.

Table 4.1. Experimentally-Determined Mode Shape Results

PEAK 1 2 3 4 5

FREQUENCY 101 121 147 135 145

MODE INDEX (1,3) (2,2) (3,1) (3,3) (1,5)

4.3 Test Plate Acoustic Characteristics

Baseline acoustic tests were performed to measure the pressure levels in the reception

chamber that were emitted from the test plate during excitation. Figure 4.7 presents these

initial results and identifies the five resonant peaks that were selected for the vibration

analysis. As with the plate vibration test results, peaks 1, 3, and 5 have high levels of

response.

50 100 150 200 250 300 350 400 45010

-2

10-1

100

101

Undamped Plate Frequency Response Function

Frequency, Hz

Pre

ssur

e/F

ram

e A

ccel

, P

a/gs

1

2

3

4

5

Figure 4.7. Acoustic Baseline Test Results for Undamped Plate

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44

Figure 4.8 shows that there is a strong correlation between the acoustic peaks and

the vibration peaks. This correlation is significant because if the vibrations are reduced,

then the radiated noise can also be reduced. Although there is a strong correlation

between the frequency of the plate vibrations and the acoustic peaks, the magnitudes of

the peaks are not necessarily correlated. In other words, the highest acoustic peaks do not

necessarily occur at the highest vibration peaks due to the effect of the plate deformation

(or mode shape) at the particular frequency. For example, in Figure 4.8, peak 2 at 121 Hz

appears to have a high vibration level, but does not seem to be a good noise radiator.

This is because the plate at this resonant peak vibrates in an even mode, as shown in

Figure 4.9.

50 100 150 200 250 300 350 400 45010

-2

10-1

100

101

102

Undamped Plate Frequency Response Function

Frequency, Hz

FR

F M

agni

tude

s, (

Pa/

g an

d g/

g)

1

2

3

4

5 Acoustic LevelsVibration Levels

Figure 4.8. Baseline Test Results Illustrating Vibration and Noise Correlation

At this frequency, there are four areas of large deformation, two of which vibrate

out of phase with the other two. Based on the acoustic theory, this causes the

equalization of air pressure from one section to the other, and therefore no pressure is

radiated away from the plate. On the other hand, if the resonant peak has an odd mode

shape, such as peak 3 illustrated in Figure 4.6, there is no equalization of pressures

because there are an odd number of vibrating sections. Therefore, acoustic pressures are

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45

radiated more efficiently from the plate. The mode shapes of peaks 1, 3, 4, and 5 are all

odd modes and are therefore efficient radiators.

Figure 4.9. Velocity Field for Peak 2 at 121 Hz From Laser Scanning Measurements

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46

4.4 Smart Plate Development

This section includes details of how and where the smart materials were applied to the

test plate, and illustrates the test setup of the smart damping plate.

4.4.1 PZT Placement and Application

The smart materials used for this research were 2.85-in square PZTs with a thickness of

0.0105 in. The PZTs (Model No. PSI-5H-S4-ENH) were acquired from Piezo Systems,

Inc. and possess the properties listed in the supplier documentation found in Appendix C.

Three of these PZTs were applied to an undamped plate, as described in Section 2.4, and

positioned as shown in Figure 4.10.

Figure 4.10. PZT Placement on the Test Plate

Figure 4.11 illustrates the locations of the PZTs for each mode shape, and the frequencies

to which shunt circuits were tuned. The PZTs were placed so that they were at the center

of the sections that deformed during vibration (i.e., at the antinodes). These were

determined to be the locations with the maximum strain, and therefore the optimum

locations for the PZTs.

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47

PEAK 1 (101 Hz) PEAK 3 (147 Hz)

DAMPED BY SHUNTING PZT C DAMPED BY SHUNTING PZT B

PEAK 4 (235 Hz) PEAK 5 (245Hz)

DAMPED BY SHUNTING PZT A DAMPED BY SHUNTING PZT A

Figure 4.11. PZT Placement and Shunting Strategy

4.4.2 Attaching PZTs to Structures

The main goal when bonding PZTs to a surface is to obtain a high level of mechanical

coupling between the PZTs and the surface. If there is good bonding contact between

them, the energy transfer from the plate to the PZT will be more efficient. For this

reason, a procedure for attaching the PZTs was developed that ensured an effective and

uniform contact between the PZTs and the plate.

The first step in this procedure is to prepare the PZTs and the plate for

application. The PZTs are electrically poled such that the top of the PZT is positive and

the bottom is negative. In order to make an electrical connection to the bottom side of the

PZT, which is bonded to the plate, thin strips of adhesive-backed copper tape are

attached. To insure a good connection between the PZTs and the copper strips, a thin

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48

layer of solder is recommended. The surface of the test plate is prepared by sanding its

surface in the areas where the PZTs are to be attached. Acetone is then used to clean the

sanded surface of metallic dust.

The next steps are to mark exactly where the PZT will be attached and to apply a

thin layer of Loctite 94 adhesive. The PZT is then set in place, while ensuring that the

copper tabs do not fold under the PZT.

Although it is not necessary, applying a vacuum over the PZT at this time would

ensure an even distribution of adhesive. The vacuum procedure setup, as illustrated in

Figure 4.12, consists of a small piece of plastic sheet, caulking tape, separator cloth,

breather cloth, and a small vacuum pump. Since the adhesive has a fast drying time, the

vacuum materials should be prepared before the adhesive is applied. A perimeter of

caulking tape is attached to the plate about 2 in around the PZT area. Next, the vacuum

pump tube is secured into this perimeter with another small piece of caulking tape. After

the adhesive is applied and the PZT is positioned, it is covered with a piece of separator

cloth and then a piece of breather cloth. This breather cloth allows the vacuum to

distribute evenly across the PZT. To seal the environment for the vacuum, a 7-in square

plastic sheet is placed over the application area and adhered to the plate with the caulking

tape perimeter. After turning on the vacuum pump, the vacuum area is checked for leaks

in the seal between the plastic and the caulking tape. The vacuum should be applied for

5-10 minutes.

When the vacuum materials are removed from the PZT and plate, wire leads are

then attached to the copper tab and top surface of the PZT. These wire leads are then

used to connect to the shunt circuit.

Figure 4.12. Vacuum Procedure Setup

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49

4.4.3 Smart Damping Plate Test Setup

Three shunt circuits were built according to the design presented in Section 2.3, and the

inductor and load resistors were set to values calculated in Section 2.3.1. A shunt circuit

was then attached to each PZT as shown in the test setup schematic in Figure 4.13(a).

Figure 4.13(b) shows the actual test setup, excluding the top enclosure, with the shunt

circuits attached to the PZTs. The shunt circuits, powered by the power supply, were

then fine-tuned, using the methods described in Appendix B, to the frequencies at which

they were designed to absorb energy.

(a) Smart Damping Plate Test Schematic

B

AC

Shunt Circuits

(b) Smart Damping Plate Test Setup, without Top Enclosure

Figure 4.13. Smart Damping Plate Testing

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50

4.5 Summary

This chapter presented the baseline tests performed on the undamped test plate and the

methods used to identify the resonant frequencies and corresponding mode shapes. The

smart damping plate development was also discussed, including the placement of the

PZTs, the attachment methodology, and the smart damping test setup.

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51

Chapter 5

Smart Damping Test Results and Benefits

This chapter presents the results of the tests conducted on the vibrations and acoustics test

stand described in Chapter 3. The purpose of this chapter is to present and compare the

vibration and structure-borne acoustic test results for a plate with and without smart

damping. This chapter also discusses the benefits of smart materials when added to

existing damping materials, as well as the weight benefits due to smart damping. The

tests were designed to compare the smart damping materials with existing damping in

terms of vibration and structure-borne noise reduction.

Figure 5.1 illustrates the different test plate configurations used to evaluate the

benefits of smart damping. The ‘undamped plate,’ which is untreated, is the standard

plate that was used for the baseline test. The ‘shunted plate’ refers to the undamped plate

with shunted PZTs. As such, the ‘unshunted plate’ is the undamped plate with PZTs

attached to it, but without the shunt circuits. Sections 5.1 and 5.2 compare the undamped

plate to the shunted and unshunted plates. The ‘damped plate’ refers to the test plate

treated with passive damping materials, while the ‘shunted damped plate’ is the damped

plate with the shunted PZTs. The benefits of adding shunted PZTs to damped plates are

investigated in Sections 5.3 and 5.4. Section 5.4 compares the shunted plate to multiple

damped plates to assess the damping benefits of smart materials with respect to added

weight.

SHUNTED UNSHUNTED UNDAMPED

UNDAMPEDTEST PLATES

W/O PZTs W/ PZTs

TEST PLATES

DAMPEDSHUNTED

DAMPEDUNSHUNTED

DAMPED

DAMPEDTEST PLATES

W/O PZTs W/ PZTs

Figure 5.1. Test Plate Configurations Used to Evaluate the Benefits of Smart Damping

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52

5.1 Vibration Benefits of Smart Damping for Undamped Plates

Once the smart damping plate was constructed, initial tests were performed on the

shunted and unshunted plates. The shunt circuits were then tuned, as described in

Chapter 2, to the resonant frequencies between 50 and 450 Hz for the unshunted plate.

Figure 5.2 illustrates the effect of the tuned shunt circuits on the plate vibration response.

Peaks 3, 4, and 5 were the most significantly reduced for the shunted plate.

50 100 150 200 250 300 350 400 45010

-1

100

101

102

Frequency Response Functions: PZT plate

Frequency, Hz

Pla

te A

ccel

/Fra

me

Acc

el, g

s/gs

1

3

4

5

Unshunted PZTsShunted PZTs

Figure 5.2. Unshunted and Shunted Plate Vibration Response

Before comparing the shunted and undamped plate responses, it is important to

first demonstrate how the frequency response of the undamped plate was altered due to

the application of the smart materials. As such, the vibration test results for the

undamped and unshunted plates are presented in Figure 5.3. The addition of the PZTs

caused a shift in some of the resonant frequencies of the unshunted plate, as is

particularly evident for peak 1 which is shifted up by approximately 15 Hz. This shift is

caused by the structural effects of PZTs, such as adding bending stiffness and slight mass

loading.

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53

50 100 150 200 250 300 350 400 45010

-1

100

101

102

Frequency Response Functions

Frequency, Hz

Pla

te A

ccel

/Fra

me

Acc

el, g

s/gs

13

4

5 Undamped PlateUnshunted PZT Plate

Figure 5.3. Effect of Adding Smart Material to an Undamped Plate

The goal of the testing was to determine the total vibration reduction achieved by

the application of smart damping. Table 5.1 presents the decreases in the peak

accelerations that were obtained using the tuned shunts. The results indicate that the

smart damping significantly reduced the four resonant peak vibrations, with the largest

reductions achieved for peaks 3 and 5. The results further show that passive smart

damping can add substantial damping for narrow-band frequencies by decreasing peak

vibrations by up to 22 dB.

Table 5.1. Effect of Smart Damping on Peak Vibrations

Peak Undamped(g/g)

Shunted PZT(g/g)

Reduction(%)

Reduction(dB)

1 (101 Hz) 57.79 31.84 56.1 5.2

3 (147 Hz) 47.74 7.53 84.6 16.0

4 (235 Hz) 11.28 4.05 64.1 8.9

5 (245 Hz) 47.97 3.87 91.9 21.9

5.1.1 Third-Octave Analysis

Another convenient method to assess the benefits of smart damping materials is to

evaluate their broadband performance using a third-octave band analysis. For the

vibration data, 1/3-octave values were determined for each center frequency according to

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54

= ∑

=

2

log10)3

1(

j

in n

n

onAcceleratiFrame

onAcceleratiPlateOctavedB (5.1)

where i and j are the lower and upper third-octave band limits, respectively, and n is the

spectral line index. Figure 5.4 shows the vibration response of the shunted and undamped

plates, and Figure 5.5 shows the broadband vibration reductions due to smart damping.

20

25

30

35

40

45

63 80 100 125 160 200 250 315Frequency, (1/3 Octave Bands)

Pla

te A

ccel

/Fra

me

Acc

el, d

B

Undamped PlateUndamped Plate w / PZTs (Shunted)

Effect of Adding Smart Damping on Undamped Plate Vibrations

Figure 5.4. Third-Octave Band Analysis of Vibrations for Undamped and Shunted Plates

-8

-6

-4

-2

0

2

4

6

8

10

12

Dec

reas

e in

Vib

ratio

ns, d

B

63 80 100 125 160 200 250 315

Frequency, (1/3 Octave Bands)

Decrease in Undamped Plate Vibrations Using Smart Damping

Figure 5.5. Decrease in Undamped Plate Vibrations (Third-Octave Band)

These figures show that smart damping can decrease the 1/3-octave accelerations

by up to 11 dB. The accelerations were not reduced in the 125-Hz octave band because

this octave band contains peak 2 at 121 Hz. As explained in Chapter 4, this peak was not

Undamped Shunted

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55

selected to be damped because it was an even mode and, therefore, an inefficient noise

radiator. Another element that contributes to the apparent lack of vibration reduction in

this band is the stiffening effect of the PZTs, as discussed in Section 5.1. As shown in

Figure 5.3, peak 1 for the undamped plate occurs at 101 Hz. When PZTs are applied to

the plate, however, this peak occurs at approximately 118 Hz, which is in the 125-Hz 1/3-

octave band. For this reason, the levels are higher for the PZT-treated plate in this

frequency band as compared to the undamped plate. For the higher peaks, the shift in

resonant frequencies is relatively smaller and the frequency bands are wider. Therefore,

the higher resonant peaks are not shifted out of the 1/3-octave bands by the addition of

PZTs.

The vibration test results show that passive smart damping can effectively reduce

vibrations for both narrowband and broadband frequency ranges by reducing acceleration

peaks by up to 22 dB, and reducing 1/3-octave values by up to 11 dB.

5.2 Acoustic Benefits of Smart Damping for Undamped Plates

To determine the effect of smart damping on structure-borne noise, the radiated acoustic

pressures were first measured for the shunted and unshunted plates and then compared to

the undamped plate. The narrowband noise levels are presented here as sound pressure

normalized with respect to frame acceleration in Pascals over g’s (Pa/g). This

normalization is performed in order to account for any frame acceleration changes that

occur from one test to another and from the addition or elimination of different materials.

Since the frame is excited by a constant force from the shaker, its acceleration changes as

the effective mass of the test plate changes.

As shown in Figure 5.6, the noise levels at the four peaks have been significantly

reduced with the most reduction occurring at peaks 3, 4, and 5. Figure 5.7 compares the

narrowband noise levels for the shunted plate with the undamped plate. The figure

clearly shows that there is a substantial reduction in noise levels due to the addition of

smart damping. The most significant reduction occurs for peak 5, where the noise levels

are reduced by 20.3 dB.

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56

50 100 150 200 250 300 350 400 45010

-1

100

101

Acoustic Levels for Smart Damping Plate

Frequency, Hz

Pre

ssur

e/F

ram

e A

ccel

, Pa/

gs 1

3

4

5

Unshunted Plate Shunted PZT Plate

Figure 5.6. Effect of Smart Damping on Structure-Borne Noise for an Undamped Plate

50 100 150 200 250 300 350 400 45010

-1

100

101

Acoustic Levels for Undamped and Shunted PZT Plates

Frequency, Hz

Pre

ssur

e/F

ram

e A

ccel

, Pa/

gs

1 3

4

5

Undamped Plate Shunted PZT Plate

Figure 5.7. Noise Reductions Due to Smart Damping of an Undamped Plate

Table 5.2 presents the decrease in the peak noise levels that were obtained using

the tuned shunts. As with the vibration test results, the table indicates that the smart

damping significantly reduces the four acoustic peaks, with the most reduction occuring

at peaks 3 and 5. The results also show that passive smart damping can add a substantial

UndampedShunted

UnshuntedShunted

Noise Levels for the Unshunted and Shunted Plates

Noise Levels for the Undamped and Shunted Plates

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57

amount of damping for narrowband frequencies by decreasing peak noise levels by up

20.3 dB, or nearly 90%.

Table 5.2. Normalized Noise Level Reductions Due to Applying Smart Damping to an Undamped Plate

Peak Undamped(Pa/g)

Shunted PZT(Pa/g)

Reduction(%)

Reduction(dB)*

1 (101 Hz) 5.27 2.26 57.1 7.4

3 (147 Hz) 5.59 1.09 80.5 14.2

4 (235 Hz) 0.55 0.37 32.7 3.4

5 (245 Hz) 3.32 0.32 90.4 20.3

*Note: Decibel scale is determined as

)/(

)/(log20

gPaLevelAcousticShunted

gPaLevelAcousticUndamped

5.2.1 Third-Octave Analysis

As with the vibration test results, a 1/3-octave band analysis was performed on the

acoustic test results to assess the broadband acoustic benefits of smart damping materials.

For acoustic analysis, it is common to present sound pressure on a decibel scale as

where Lp is referred to as the sound pressure level, or SPL, and

Pref = 20e-6 Pa [28].

This decibel calculation, which is performed on the microphone pressure

measurements of the reception chamber, discounts the mass-loading effect of the added

PZTs on the input frame acceleration. This analysis is, therefore, only valid for

evaluating the acoustic effects of adding the shunt circuits to the unshunted test plate

since the circuits do not load the plate or frame. This analysis has been included here in

order to provide a subjective feel for the noise level range occurring in the reception

chamber during experimentation.

For the unshunted and shunted acoustic data, third-octave sound pressure levels

were determined for each center frequency as

)(log20 dBP

PL

ref

rmsp

= (5.2)

Page 68: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

58

)(log10)3

1(

2

dBP

POctaveL

j

in ref

rmsp

= ∑

= (5.3)

where i and j are the lower and upper third-octave band limits, respectively, and n is the

spectral line index. Figure 5.8 presents the third-octave band analysis performed on the

shunted and unshunted PZT plate sound pressure levels. Figure 5.9 represents the

decrease in SPLs obtained at each third-octave band. The most SPL reductions of 3 to 5

dB occurred in the 125 Hz, 160 Hz, and 250 Hz third-octave bands. This was to be

expected since these are the bands where the shunt circuits were designed to operate. The

total sound pressure levels for all 8 third-octave bands were determined to be 61.07 dB

and 59.13 dB for the unshunted and shunted test plates, respectively. The total

broadband noise reduction achieved with the addition of the shunt circuits was 1.94 dB.

42

47

52

57

63 80 100 125 160 200 250 315Frequency, (1/3 Octave Bands)

SP

L, d

B (

ref 2

0e-6

Pa)

Unshunted PZTShunted PZT

Effect of Adding Smart Damping on Structure-Borne Noise

Figure 5.8. Third-Octave Band Analysis of Structure-Borne Noise for an Undamped Plate

-2

-1

0

1

2

3

4

5

Dec

reas

e in

SP

L, d

B

63 80 100 125 160 200 250 315

Frequency, (1/3 Octave Bands)

Decrease in Structure-Borne Noise Using Smart Damping

Figure 5.9. Decrease in Structure-Borne Noise for an Undamped Plate (Third-Octave Band)

Page 69: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

59

In order to accurately compare the shunted plate and undamped plate acoustic

levels and discount the mass loading effects, the acoustic data must then be presented as

acoustic pressure over frame acceleration in Pa/g. Therefore, the new dB scale

)()/(20

)/(/Prlog20

6dB

gPae

gPaAccelessNSPL

ref

rms

= − (5.4)

was used to perform a third-octave band analysis on the undamped and shunted test data.

Figures 5.10 and 5.11 present the third-octave analysis for acoustic levels of the

undamped plate and the shunted smart damping plate. It is evident from Figure 5.10 that

the addition of smart damping can reduce the NSPL (normalized sound pressure levels)

from the test plate by up to 7.9 dB. The smart damping had the most effect in the 160-

and 250-Hz third-octave bands. The total NSPLs for all 8 third-octave bands were

determined to be 118.04 dB and 114.34 dB for the undamped and shunted test plates,

respectively. The total broadband noise reduction achieved with the addition of the smart

damping was 3.7 dB.

As with the vibration results presented in the previous section, the increase in

NSPLs for the 125-Hz third-octave band is caused by the shift in frequency of peak 2.

95

100

105

110

115

63 80 100 125 160 200 250 315Frequency, (1/3 Octave Bands)

NS

PL,

dB

, (re

f 20e

-6 P

a/g

)

Undamped Plate

Undamped Plate w/ PZTs (Shunted)

Effect of Addin g Smart Dam ping on Normalized Sound Pressure Levels

Figure 5.10. Third-Octave Band Analysis for Undamped and Shunted Plates

Undamped Shunted

Page 70: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

60

-6

-4

-2

0

2

4

6

8

Dec

reas

e in

NS

PL,

dB

63 80 100 125 160 200 250 315

Frequency, (1/3 Octave Bands)

Decrease in Normalized Sound Pressure Levels Using Smart Damping

Figure 5.11. Decrease in Acoustic Levels Using Smart Damping

As expected and also shown in Figure 5.12, in each band, the NSPL reductions directly

correspond to the vibration reductions which were discussed earlier. Therefore, it can be

concluded that smart passive damping of structural vibrations can yield significant

reductions in structure-borne noise.

-8

-6

-4

-2

0

2

4

6

8

10

12

Red

uctio

ns, d

B

63 80 100 125 160 200 250 315

Frequency, 1/3 Octave Bands

Correlation of Vibration and Structure-Borne Noise Reductions

Acoustic Reductions

Vibration Reductions

Figure 5.12. Correlation of Plate Vibration Reductions to Structure-Borne Noise Reductions

Page 71: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

61

5.3. Benefits of Smart Damping for Damped Structures

This section investigates the added benefits of applying smart damping when used with

conventional passive damping materials. The effect of adding smart damping materials

to a plate damped with

• unbacked carpet,

• shoddy and unbacked carpet, and

• shoddy and 0.3 PSF backed carpet

was evaluated. The evaluation was based on comparing the noise and vibration

measurements with and without smart damping for each of the above treatments. These

treatments, as shown in Figure 5.13, were cut into 400 mm x 500 mm samples that were

placed over the test plates. Each material is evaluated by measuring the plate vibrations

and emitted noise, similar to the undamped cases.

Shoddy is a foam pad made of interwoven fabric scraps that is placed under the

carpeting in vehicles. The backed carpet has a layer of rubber melted onto the carpet to

add damping with mass loading. The grade of carpet is measured as pounds per square

foot or PSF.

Shoddy

0.3 PSFBackedCarpet

Unbacked Carpet

500 mm

400 mm

Figure 5.13. Passive Treatments Used with Smart Damping Materials

Page 72: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

62

As was expected, the damping treatments altered the frequency response of the plate

which required the shunts to be retuned for each damping case. Once the shunt circuits

were optimized, the three different treatments were tested for both the shunted plate and

the undamped plate. The augmenting vibration benefits of PZTs are presented first

followed by the acoustic benefits.

5.3.1 Vibration Benefits of Adding Smart Damping to Damped Structures

The third-octave analysis of the vibration responses of the undamped and smart damping

plates with the different damping treatments is presented in Figure 5.14. Figure 5.15

shows the vibration reductions achieved for each third-octave band using smart damping.

The test results for the smart damping plate and the undamped plate without treatment

have been included in these figures to illustrate the baseline test results obtained in the

previous section.

It is evident in Figures 5.14 and 5.15 that the smart damping has the most effect

on accelerations above 125 Hz. It is also noted that the PZTs add less additional damping

as the amount of treatment increases and the vibrations decrease. For the unbacked

carpet case, there is no decrease in vibrations at 125 Hz due to the same reasons

mentioned in the baseline test results. In the 100-Hz third-octave band, it appears that the

addition of the treatments has little effect on the smart damping plate vibrations as

compared to the undamped plate. When the treatments are tested with the smart damping

plate, they are laid over the PZTs, the copper tabbing, and the wiring. This yields a poor

contact between the treatment and the plate, and therefore reduces the vibration damping

benefits of the treatments.

Page 73: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

63

20

25

30

35

40

45

63 80 100 125 160 200 250 315Fr e q u e n cy, (1/3 Octave Ban d s )

Pla

te A

ccel

/Fra

me

Acc

el, d

B

No Treatment (w /o PZT)No Treatment (w / PZ T)

Additiona l Da m ping Due to S m a rt Da m ping

(a) No Treatment

20

25

30

35

40

45

63 80 100 125 160 200 250 315Fr e q ue n cy, (1/3 Octave Ban d s )

Pla

te A

ccel

/Fra

me

Acc

el, d

B

Unbacked Carpet (w /o PZ T)Unbacked Carpet (w / PZ T)

Additiona l Da m ping Due to S m a rt Da m ping

(b) Unbacked Carpet

20

25

30

35

40

45

63 80 100 125 160 200 250 315Fr e q u e n cy, (1/3 Octave Ban d s )

Pla

te A

ccel

/Fra

me

Acc

el, d

B

Shoddy+ Unbac ked Carpet (w /o PZT)Shoddy+ Unbac ked Carpet (w / PZ T)

Additiona l Da m ping Due to S m a rt Da m ping

(c) Shoddy + Unbacked Carpet

20

25

30

35

40

45

63 80 100 125 160 200 250 315Fre que ncy, (1/3 Octave Bands )

Pla

te A

ccel

/Fra

me

Acc

el, d

B

Shoddy + 0.3PSF Carpet (w /o PZT)Shoddy + 0.3PSF Carpet(w / PZT)

Additiona l Dam ping Due to Smart Dam ping

(d) Shoddy + 0.3 PSF CarpetFigure 5.14. Vibration Benefits of Smart Damping Materials for a Damped Plate

Undamped Shunted

Damped Damped Shunted

Damped Damped Shunted

Added Damping Due to Smart Damping (Unbacked Carpet)

Added Damping Due to Smart Damping (No Treatment)

Added Damping Due to Smart Damping (Shoddy +Unbacked Carpet)

Damped Damped Shunted

Added Damping Due to Smart Damping (Shoddy +0.3 PSF Carpet)

Page 74: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

64

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 8

- 6

- 4

- 2

0

2

4

6

8

1 0

1 2

Dec

reas

e in

Vib

ratio

n Le

vels

, dB

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5

F r e q u e n c y , ( 1 /3 O c t a v e Ba n d s )

D e c r e a se i n V i b ra ti o n L e v e l s U si n g S m a r t D a m p i n g

U n d a m p e d

(a) No Treatment

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 6

- 4

- 2

0

2

4

6

8

1 0

Dec

reas

e in

Vib

ratio

n Le

vels

, dB

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5

F r e q u e n c y , ( 1 /3 O c t a v e Ba n d s )

D e c r e a se i n V i b ra ti o n L e v e l s U si n g S m a r t D a m p i n g

U n b a c ke d C a r p e t

(b) Unbacked Carpet

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 4

- 3

- 2

- 1

0

1

2

3

4

Dec

reas

e in

Vib

ratio

n Le

vels

, dB

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5

F r e q u e n c y , 1 /3 O c t a v e Ba n d s

D e c r e a se i n V i b ra ti o n L e v e l s U si n g S m a r t D a m p i n g

S h o d d y + Un b a c k e d C a r p e t

(c) Shoddy + Unbacked Carpet

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 4

- 3

- 2

- 1

0

1

2

3

Dec

reas

e in

Vib

ratio

n Le

vels

, dB

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5

F r e q u e n c y , 1 /3 O c t a v e Ba n d s

D e c r e a se i n V i b ra ti o n L e v e l s U si n g S m a r t D a m p i n g

S h o d d y + 0 .3 PS F C a r p e t

(d) Shoddy + 0.3 PSF CarpetFigure 5.15. Vibration Decrease due to Smart Damping Materials Applied to a Damped Plate

Dec

reas

e in

Acc

eler

atio

n, (

dB)

Dec

reas

e in

Acc

eler

atio

n, (

dB)

Dec

reas

e in

Acc

eler

atio

n, (

dB)

Dec

reas

e in

Acc

eler

atio

n, (

dB)

Decrease in Acceleration Using Smart Damping

Decrease in Acceleration Using Smart Damping

Decrease in Acceleration Using Smart Damping

Decrease in Acceleration Using Smart Damping

Frequency, 1/3 Octave Bands

Frequency, 1/3 Octave Bands

Frequency, 1/3 Octave Bands

Frequency, 1/3 Octave Bands

Page 75: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

65

5.3.2 Acoustic Benefits of Adding Smart Damping to Damped Structures

A third-octave analysis, using the decibel scale in Equation (5.2), was performed on the

sound pressure measurements of the undamped and smart damping plates with the

different damping treatments. These results are presented in Figure 5.16. Figure 5.17

shows the NSPL reductions achieved for each third-octave band using smart damping.

The test results for the smart damping plate and the undamped plate without treatment

have been included in these figures to illustrate the baseline test results obtained in the

previous section.

These results show that smart damping has the most added damping effect for the

160- and 250-Hz third-octave bands. As with the vibration analysis, it is also evident that

the PZTs add less noise reduction as the amount of treatment increases. It is noted that

the addition of shoddy or 0.3 PSF backed carpet has no added effect on the NSPLs for the

shunted plate. This is either because of the poor contact with the plate caused by the

PZTs or the added stiffness of the PZTs. Further, as addressed in Section 2.1, the

negative value at 125 Hz is caused by the shifting of the resonant frequency of peak 1

from the 100-Hz frequency band to the 125-Hz frequency band.

Overall, the damped shunted plate contributes a notable amount of structure-borne

noise reduction. For the unbacked carpet case, the smart damping decreases the NSPLs

by an average of 2.6 dB. For the plate treated with shoddy and unbacked carpet, the

average added reduction is 2.2 dB, and for the shoddy- and-0.3-PSF-damped plate, the

average added reduction is 0.9 dB.

Page 76: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

66

90

95

100

105

110

115

63 80 100 125 160 200 250 315Frequency, (1/3 Octave Bands)

Pre

ss/F

ram

e A

ccel

, dB

, (re

f 20

e-6

Pa/

g)

No Treatment (w /o PZT)No Treatment (w / PZT)

Additional Damping Due to Smart Damping

(a) No Treatment

90

95

100

105

110

115

63 80 100 125 160 200 250 315Fre que ncy, (1/3 Octave Bands )

Pre

ss/F

ram

e A

ccel

, dB

, (re

f 20

e-6

Pa/

g)

Unbacked Carpet (w /o PZT)

Unbacked Carpet (w / PZT)

(b) Unbacked Carpet

90

95

100

105

110

115

63 80 100 125 160 200 250 315Fr e qu e n cy, (1 /3 Octave Band s )

Pre

ss/F

ram

e A

ccel

, dB

, (re

f

20e-

6 P

a/g)

Shoddy + Unbac ked Carpet(w /o PZ T)Shoddy + Unbac ked Carpet (w / PZ T)

(c) Shoddy + Unbacked Carpet

90

95

100

105

110

115

63 80 100 125 160 200 250 315Fr e qu e n cy, (1/3 Octave Band s )

Pre

ss/F

ram

e A

ccel

, dB

, (re

f

20e-

6 P

a/g)

Shoddy + 0.3PSF Carpet (w /o PZ T)

Shoddy + 0.3PSF Carpet (w / PZ T)

(d) Shoddy + 0.3 PSF Carpet Figure 5.16. Acoustic Benefits of Smart Damping Materials for a Damped Plate

Added Noise Reductions Due to Smart Damping (Shoddy +Unbacked Carpet)

Added Noise Reductions Due to Smart Dam ping (Shodd y + 0.3 PSF Carpet)

Added Noise Reductions Due to Smart Damping (Unbacked Carpet)

Added Noise Reductions Due to Smart Damping (No Treatment)

Undamped Shunted

Damped Damped Shunted

Damped Damped Shunted

Damped Damped Shunted

NS

PL,

(dB

), (

ref

20e-6

Pa/

g)N

SP

L, (

dB),

(re

f 20

e-6 P

a/g)

NS

PL,

(dB

), (

ref

20e-6

Pa/

g)N

SP

L, (

dB),

(re

f 20

e-6 P

a/g)

Page 77: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

67

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 6

- 4

- 2

0

2

4

6

8

Dec

reas

e in

Aco

ustic

Lev

els,

dB

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5

F r e q u e n c y , ( 1 /3 O c t a v e B a n d s )

D e c r e a se i n A c o u st i c L e v e l s U si n g S m a r t D a m p i n g

U n d a m p e d

(a) No Treatment

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 1

0

1

2

3

4

5

6

7

Dec

reas

e in

Aco

ustic

Lev

els,

dB

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5

Fr e q u e n c y , ( 1 /3 O c t a v e Ba n d s )

D e c r e a se i n A c o u sti c L e v e l s U si n g S m a rt D a m p i n g

Un b a c ke d Ca r p e t

(b) Unbacked Carpet

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 2

- 1

0

1

2

3

4

5

6

7

Dec

reas

e in

Aco

ustic

Lev

els,

dB

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5

F r e q u e n c y , 1 /3 O c t a v e Ba n d s

D e c r e a se i n A c o u sti c L e v e l s U si n g S m a rt D a m p i n g

S h o d d y + Un b a c k e d C a r p e t

(c) Shoddy + Unbacked Carpet

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 5

- 4

- 3

- 2

- 1

0

1

2

3

4

5

6

Dec

reas

e in

Aco

ustic

Lev

els,

dB

6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5

Fr e q u e n c y , 1 /3 O c t a v e Ba n d s

D e c r e a se i n A c o u sti c L e v e l s U si n g S m a rt D a m p i n g

S h o d d y + 0 .3 PS F Ca r p e t

(d) Shoddy + 0.3 PSF CarpetFigure 5.17. Decrease in NSPL due to Smart Damping Materials Applied to a Damped Plate

Dec

reas

e in

NS

PL,

(dB

)D

ecre

ase

in N

SP

L, (

dB)

Dec

reas

e in

NS

PL,

(dB

)D

ecre

ase

in N

SP

L, (

dB)

Decrease in Normalized Sound Pressure Levels Using Smart Damping

Decrease in Normalized Sound Pressure Levels Using Smart Damping

Decrease in Normalized Sound Pressure Levels Using Smart Damping

Decrease in Normalized Sound Pressure Levels Using Smart Damping

Frequency, 1/3 Octave Bands

Frequency, 1/3 Octave Bands

Frequency, 1/3 Octave Bands

Frequency, 1/3 Octave Bands

Page 78: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

68

5.4 Weight Saving Benefits of Smart Damping Materials

One of the design elements that is often considered in the automotive industry is the

weight savings for different vibration and acoustic solutions. For this reason, this section

examines the performance of various treatments normalized to the amount of weight they

add. To this end, a series of tests were run using eight different combinations of

treatments as shown in Table 5.3.

Table 5.3. Different Treatments Tested with Smart Damping

Test#

ViscoelasticTreatments

Foam Pads Carpeting Typical PackageType

1 None No Pad Unbacked Carpet Worst

2 None Shoddy Unbacked Carpet Economy

3 None Shoddy 0.3 PSF Backed Carpet Mid-size Sedan

4 Asphalt Shoddy 0.3 PSF Backed Carpet Family Car

5 Asphalt 2.5 PCF Foam 0.3 PSF Backed Carpet Sport Utility

6 Asphalt 2.5 PCF Foam 0.3 PSF Backed Carpet Luxury SportUtility

7 Constrained Layer (CLD) (Masdamp 755)

2.5 PCF Foam 0.3 PSF Backed Carpet Luxury Sedan

8 Constrained Layer (CLD) (Masdamp 755)

2.5 PCF Foam 0.7 PSF Backed Carpet Best

Figure 5.18(a) shows the two types of viscoelastic damping treatments, commonly used

in vehicles, that were evaluated for this test. Constrained layer damping, illustrated in

Figure 5.18(b), has an aluminum foil backing and a viscoelastic material that is a

pressure-sensitive adhesive. The asphalt damping material is the most commonly used

treatment in the automotive industry and is either melted onto the surface or attached with

contact cement. For this test, the asphalt was attached with contact cement.

Figure 5.19 shows the types of commonly used foam pads and carpeting that were

tested to assess the weight-saving benefits of smart damping. These treatments are

placed over the different damped plates with the foam padding between the plate and the

carpet.

Page 79: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

69

(a) Constrained Layer and Asphalt Damped Plates (b) Constrained Layer Damping

Figure 5.18. Damping Treatments Applied to Test Plates

CarpetingFoam Pads

2.5 PCF Shoddy Unbacked 0.3 PSFBacked

0.7 PSFBacked

Figure 5.19. Different Foam Pads and Carpeting Damping Treatments

For each case, the vibration and acoustics reductions were normalized to the

added weight due to the treatment, i.e.

))(,(

))(,(

lbWeightAdded

dBonsAccelerati∆ (5.5)

and

))(,(

))(,(

lbWeightAdded

dBNSPL∆. (5.6)

Page 80: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

70

The added weights of the different treatments are shown in Table 5.4

Table 5.4. Weights of Different Treatments

Plate Treatment Tested Weight(lb)

Weight ofAdded

Treatment(lb)

WeightIncrease

(%)

Undamped Plate 4.72 Baseline Baseline

Undamped Plate w/ PZTs 4.82 0.11 2.33

Unbacked Carpet 4.94 0.23 4.87

Shoddy and Unbacked Carpet 5.49 0.78 16.5

Shoddy and 0.3 PSF Backed Carpet 6.09 1.37 29.0

Asphalt, Shoddy, and0.3 PSF Backed Carpet

7.59 2.87 60.8

Asphalt, 2.5 PCF Foam, and 0.3 PSF Backed Carpet

7.50 2.78 58.9

Asphalt, 2.5 PCF Foam, and0.7 PSF Backed Carpet

8.30 3.58 75.5

CLD, 2.5 PCF Foam, and 0.3 PSF Backed Carpet

7.07 2.36 50.0

CLD, 2.5 PCF Foam, and 0.7 PSF Backed Carpet

7.87 3.15 66.7

The differential vibration and acoustic reductions, and the differential weights are all

computed with respect to the undamped plate. As the results of Figures 5.20 and 5.21

show, the PZT treatments offer the most noise and vibration benefits with respect to the

weight they add to the structure. This is especially true when the weight benefits of

smart damping are compared to the plates damped with a viscoelastic layer. The

reduction per weight benefits of the PZTs are more than 10 times those of these

treatments. Although these treatments can be very effective, a minimum of 50% weight

increase is required to achieve the desired damping levels. These test results show that

smart damping could replace the viscoelastic damping without the added weight.

Page 81: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

71

Figure 5.20. Decrease in Accelerations with Respect to Added Weight

6380

100125

160

200

250

315

-60

-40

-20

0

20

40

60

80

100

Pla

te A

ccel

/Fra

me

Acc

el, D

elta

dB

/lb

(Und

ampe

d P

late

as

Bas

elin

e)

Center Frequencies, 1/3 Octave Bands

Weight Saving Effects of PZT's:Decrease in Accelerations/Weight

Undamped Plate w/Unbacked Carpet

Undamped Plate w/Shoddy + UnbackedCarpet

Undamped Plate w/Shoddy + 0.3 PSFBacked Carpet

Asphalt Plate w/Shoddy+ 0.3 PSFBacked Carpet

Asphalt Plate w/ 2.5 PCF Foam + 0.3PSF Backed Carpet

Asphalt Plate w/ 2.5 PCF Foam + 0.7PSF Backed Carpet

CLD Plate w/ 2.5 PCF Foam+ 0.3PSF Backed Carpet

CLD Plate w/ 2.5 PCF Foam + 0.7PSF Backed Carpet

Shunted Plate (no Treatment)

Page 82: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

72

6380

100125

160200

250315

-60

-40

-20

0

20

40

60

80

NS

PL/

Wei

ght,

Del

ta d

B/lb

(U

ndam

ped

Pla

te a

s B

asel

ine)

Frequency, 1/3 Octave Bands

Weight Saving Effects of PZTs:Decrease in Normalized Sound Pressure Levels/Weight

Undamped Plate w/Unbacked Carpet

Undamped Plate w/Shoddy + UnbackedCarpet

Undamped Plate w/Shoddy + 0.3 PSFBacked Carpet

Asphalt Plate w/Shoddy+ 0.3 PSFBacked Carpet

Asphalt Plate w/ 2.5 PCF Foam + 0.3PSF Backed Carpet

Asphalt Plate w/ 2.5 PCF Foam + 0.7PSF Backed Carpet

CLD Plate w/ 2.5 PCF Foam+ 0.3PSF Backed Carpet

CLD Plate w/ 2.5 PCF Foam + 0.7PSF Backed Carpet

Shunted Plate (no Treatment)

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73

5.5 Summary

The benefits of smart damping materials, specifically piezoceramics with shunt circuits,

in reducing vibrations and structure-borne noise were addressed. Using the test rig

described in Chapter 3, a series of tests were conducted on a test plate with shunted PZTs.

A comparison of the results with an undamped plate showed that the smart damping

materials can significantly lower both the plate vibration and the structure-borne noise for

both narrowband and broadband frequencies. The augmenting benefits of adding smart

damping to commonly used damping treatments were presented, as well the weight-

saving benefits of PZTs.

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74

Chapter 6

Transmission Loss Tests

This chapter describes and presents the experimental setup, test calibration, and test

results for the transmission loss tests that were performed to further evaluate the

performance of the smart damping plate. These tests were conducted at an SAE J1400

transmission loss test facility according to the details of the SAE J1400 standardized test

specifications entitled ‘Laboratory Measurements of the Airborne Sound Barrier

Performance of Automotive Materials and Assemblies’ [30]. The transmission loss test

facility has two adjacent rooms, a reverberation room and a semi-anechoic reception

room. A test window is located between the two rooms where test panels are placed for

testing. Sound is generated in the reverberation room, and the amount of sound

transmitted through the window is measured.

6.1 Test Setup

The SAE J1400 test facility, the floor plan of which is illustrated in Figure 6.1, consists

of a 300-cubic meter-reverberation room, a semi-anechoic reception chamber, and a

joining wall.

Figure 6.1. Floor Plan of Transmission Loss Test Facility

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75

For testing, a test panel with a variety of different damping materials is inserted in

a window located in the joining wall. The window, originally adapted for a 3 ft x 3 ft test

panel, had to be modified to accommodate the smaller 0.6m x 0.5m standard test plate, as

documented in Appendix E. The new test window, shown in Figure 6.2, was built to

simulate the same fully-clamped boundary conditions as described for the vibration and

acoustics tests.

Figure 6.2. Modified Test Window, Reverberation Room Side

Initial tests were run with this window in order to calibrate the data acquisition

program that measures the noise reduction and calculates the panel transmission loss.

Once the test setup was calibrated, transmission loss tests were conducted for three

different test plates:

• a standard test plate,

• a PZT plate, and

• a PZT plate (PZTs not shunted) with constrained layer damping.

6.2 Transmission Loss Calibration Tests

For lab measurements, transmission loss is determined using the equation

TL = MNR + 10log10(A/Sα) (6.1)

ModifiedTestWindow

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76

where TL is the transmission loss of the panel, MNR is the measured noise reduction

between the reverberation room and reception chamber, Sα is the Sabine absorption of

the receiving room, and A is the area of the test window. The expression 10log10(A/Sα)

is constant for any test panel with the same area. Therefore, it can be replaced with a

constant correction factor, CF, which modifies Equation (6.1) to

TL = MNR - CF (6.2)

To determine this correction factor for the new window, a flexible test sample, as

depicted in Figure 6.3, was made out of 2mm-thick barrier material to clamp into the test

window. The transmission loss of the barrier material from 100-10,000 Hz can be

directly calculated from the mass-law equation:

TLcalc(dB)= 20log10(W) + 20log10(f) -47.2 (6.3)

where Tlcalc is the theoretical transmission loss, W is the weight density of the panel, and f

is the center frequency of the third-octave measurement band.

Calibration Test Panel

Window Adapter

Figure 6.3. Modified Test Window with Barrier Material for Calibration Test

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77

To determine the correction factor, speakers placed in the reverberation room

generate a white noise with a bandwidth of 100 to 10,000 Hz. The noise level is recorded

in the reverberation chamber and the reception chamber by microphones. The difference

of these measurements minus the measured ambient sound levels is recorded as MNR.

The correction factor, CF, is then determined for each third-octave band center

frequency as

CF = MNR - TLcalc. (6.4)

The data acquisition program then stored these correction factors to calculate the

transmission loss of the test plates. For example, after the measured noise reduction for

the standard test panel, i.e. MNRstd, is recorded, the program computes the transmission

loss as

TLstd = MNRstd - CF. (6.5)

6.3 Transmission Loss Testing and Results

Three different test plates were used for the transmission loss tests. Just as in the

vibration and acoustics test stand, each plate was clamped into the test window by

tightening the 14 bolts to a torque of 25 N-m. The first plate tested was the standard test

plate used for the vibration and acoustics tests. The second plate was the PZT plate with

the shunting circuits. The third plate was the same PZT plate with constrained layer

damping (MASDAMP755) added to its backt. This third plate was tested without the

shunting circuits. The purpose of testing this third plate was to test the effects of adding

damping against the effect of shunting the PZTs.

6.3.1 Tuning the PZT Shunts

Once the PZT test plate was clamped into the test window, as shown in Figure 6.4, with

the wiring in place, the PZT shunts had to be tuned, as described in Appendix B, to the

resonant frequencies of the plate.

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78

Figure 6.4. Undamped Plate with Smart Damping in Modified Test Window,Reception Chamber Side

In order to set the inductors to the required values, the frequencies of the resonant

peaks were determined. The narrowband frequency response function for the plate was

generated using a small impact hammer and an accelerometer. The accelerometer

measurement was taken at the center of the plate, and the hammer impact position was in

the center of the top third part of the plate. The frequency response of the PZT plate in

the test window was slightly different from the response generated by the vibration and

acoustics test stand. This was due to the fact that the test window boundary conditions

were different than the structure-borne test stand boundary conditions. For instance, as

shown in Figure 6.5, the peak at approximately 160 Hz is much smaller than the peaks at

120, 240, and 260 Hz, which was not the case in the vibration and acoustics test stand.

The shunt circuits were therefore tuned again in the J-1400 test window as shown

in Figure 6.5. The shunt circuits were tuned for the same peaks as the vibration stand

tests. The peak at 190 Hz was an even mode that was not chosen to be reduced.

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79

UnshuntedShunted

100 150 200 250 3000

20

40

60

80

100

120

140Frequency Response: accel/force, Shunted and Unshunted PZT Plate

Frequency, Hz

Mag

nitu

de, g

s/lb

Figure 6.5. Plate Vibrations with Unshunted and Shunted PZT’s

6.3.2 Transmission Loss Test Results

After the shunt circuits were tuned, the transmission loss at a single frequency was tested

to determine the effect of attaching the shunt circuits to the smart damping plate. A

single tone at 162.75 Hz (peak 3) was generated by the speakers in the reverberation

chamber, and the transmitted sound pressure was measured in the reception room. Figure

6.6 shows the time trace of the reception room sound pressure as the shunts are turned on.

The shunt circuits decreased the sound pressure levels by approximately 5.8 dB.

1

3

45

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80

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04 Reception Microphone Signal, Effect of Shunting at 162.75 Hz,

Sou

nd P

ress

ure,

Pa

Time, s

SHUNT OFF (SPL=65.3 dB)

SHUNT ON (SPL=59.5 dB)

Figure 6.6. Sound Pressure in Reception Chamber Before and After Turning on the Shunt Circuits

The PZT plate was then tested without shunting and with shunting to determine how

much smart damping increases the transmission loss for 100-10,000 Hz. The PZT plate,

however, was only designed to increase the transmission loss from 100-300 Hz. Figure

6.7 shows the test results for the entire frequency range.

Transmission Loss: Unshunted vs Shunted PZT Plate

0

5

10

15

20

25

30

35

40

45

100

125

160

200

250

315

400

500

630

800

1000

1250

1600

2000

2500

3150

4000

5000

6300

8000

10000

Frequency (1/3 Octave Band)

TL

(dB

)

PZT Plate (unshunted)

PZT Plate (shunted)

Figure 6.7. Transmission Loss for Test Plate with Unshunted and Shunted PZTs

SHUNT OFF (SPL = 65.3 dB) SHUNT ON (SPL = 59.5 dB)

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81

As expected, the figure shows that smart damping does not increase the transmission loss

for frequency bands over 400 Hz. Figure 6.8 also shows that smart damping has the most

significant effect in the 125Hz and 250 Hz third-octave bands. These shunt circuits were

designed to operate in these frequency bands. Figure 6.8, which more clearly shows the

results for the 100-400 Hz frequency range, illustrates that smart damping can add up to 7

dB of transmission loss.

Transmission Loss: Unshunted vs Shunted PZT Plate

0

5

10

15

20

25

100 125 160 200 250 315 400Frequency (1/3 Octave Band)

TL

(dB

)

PZT Plate (unshunted)

PZT Plate (shunted)

Figure 6.8. Transmission Loss for Test Plate with Unshunted and Shunted PZTs

The performance of the smart plate was also evaluated by comparing the shunted

PZT plate with no damping to the same PZT plate that is unshunted and has constrained

layer damping attached on the entire back of the plate. For the analysis, the transmission

loss data of the PZT plate with constrained layer damping was scaled to eliminate the

mass loading effects of the damping material. From Equation 6.3, the added transmission

loss due to the weight of the panel is

TLmass = 20log10(W). (6.6)

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82

For the PZT plate, with a weight density of 7.413 kg/m² , this mass loading factor, TLmass,

equals 17.40 dB. For the PZT plate with constrained layer damping and with a weight

density of 9.600 kg/m² ,

TLmass = 19.64 dB. (6.7)

Therefore, the additional transmission loss created by the mass of the constrained layer

damping is 2.24 dB. Figure 6.9 shows the final transmission loss results with the added

weight factored out.

Transmission Loss

0

5

10

15

20

25

30

35

40

45

100

125

160

200

250

315

400

500

630

800

1000

1250

1600

2000

2500

3150

4000

5000

6300

8000

1000

0

1/3 Octave Band Center Frequencies, Hz

Tra

nsm

issi

on L

oss,

(dB

)

Unshunted PZT Plate w/o CLDShunted PZT Plate w/o CLDUnshunted PZT Plate w/ CLD (Weight Corrected)

Figure 6.9. Transmission Loss Results of Shunted and Unshunted PZT Plate with Constrained Layer Damping

To further compare the performance of the smart damping materials and constrained

layer damping materials, the transmission loss benefits per added weight of the materials

were determined:

∆∆

∆∆

( )

( )

( )

( )

TransmissionLoss

AddedWeight

TL

W= (6.8)

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83

For each case, the differential transmission loss and weight were calculated as

∆(TL) = TL|treated plate - TL|standard plate (6.9)

∆(W) = W|treated plate - W|standard plate (6.10)

The results shown in Figure 6.10 indicate that the smart damping materials have a

significantly larger transmission loss to weight ratio at all of the frequencies for which

they are tuned (i.e., 125, 160, and 250 Hz) than passive damping treatments. The

implication of the results in Figure 6.10 is that smart damping materials can potentially

be used to provide a higher transmission loss at selected frequencies without any

significant amount of added weight to the vehicle.

Gain in Transmission Loss Relative to In creased We ight

-10

-5

0

5

10

15

20

25

30

35

40

125 160 200 250 315

1/3 Octave Band Center Frequencies, Hz

Del

ta T

L/W

eigh

t, (

dB/lb

)

Unshunted PZT Plate w/ CLDShunted PZT Plate w/o CLD

Figure 6.10. Increased Transmission Loss Normalized with Respect to Added Weight

6.4 Summary

The results for the transmission loss tests performed at the SAE J1400 standardized test

facility of the Lear Corporation acoustical lab were presented. The test window was

modified to test the undamped and smart damping plates that were used for the vibration

and structure-borne noise tests. It was shown that the addition of smart damping can

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84

increase the transmission loss of the plate by up to 7 dB. It was also shown that this

transmission loss can be achieved while adding a minimal amount of weight to the plate.

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85

Chapter 7

Conclusions

7.1 Summary

A special test rig was constructed and validated for the purpose of achieving the

objectives of this study, which included evaluating the feasibility and noise, vibration,

and harshness effectiveness (NVH) of smart damping materials for augmenting the

performance of passive damping materials. Passive damping materials fulfill a role that

the passive dampers cannot perform: damping at selected discrete frequencies. The tests

further included SAE J1400 tests, conducted at a transmission loss test facility, in order to

evaluate the effects of smart materials on sound transmission loss. The test results

indicated that, with the application of smart damping, it is possible to decrease

• vibration peaks by up to 22 dB,

• broadband vibrations by up to 11 dB, and

• broadband sound pressure levels by up to 4.7 dB SPL.

The test results further indicated strong commercial potentials for smart damping

materials in terms of

1. extending the benefits of the passive damping treatments used currently for

automotive markets, and

2. providing equivalent or improved performance at selected frequencies with

weight savings as measured by noise and vibration reduction per added

weight, in comparison with passive damping treatments.

7.2 Recommendations for Future Research

The test results identified strong potential benefits of smart damping materials for

multiple applications. In addition to automotive and aerospace applications, smart

damping treatments that were considered in this study can be used in other applications

such as home appliances, disk drives, and microelectronic components.

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86

Another area that deserves further investigation is evaluating alternative shunting

techniques, such as those mentioned in the literature review of Section 2.3, for better

control of vibration in various structural and acoustical modes. For example, more tests

should be conducted with the alternative shunt design with a parallel RL circuit that was

investigated by Wu [20] and the multi-mode shunt circuit demonstrated by Wu and Bicos

[21]. An alternate shunt method might reduce the time required for the tuning process

and a multi-mode shunt will reduce the number of PZTs required for the same amount of

damping. Another method that might help expedite the tuning process would be to utilize

a data acquisition system that can provide a real-time response so that the shunt

components can be continuously tuned. More research should also be performed on the

optimization of piezoceramic placement and modeling. In practical applications, it is

more difficult to experimentally determine areas of high strain for vibrating structures

that are more complicated than a plate. Finite element modeling could prove to be useful

in determining these areas that are ideal for PZT placement. The finite element model

could also be used to theoretically predict the damping performance of different PZT

configurations.

For future research in regards to the research presented in this paper, the ultimate

benefits and application of smart materials should be determined by applying the

materials to actual automotive structures in the field, laboratory, or both. A more

complex structure such as a stripped car body, a ‘body-in-white,’ would be ideal for

future research on the application of smart damping for automotive benefits.

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87

References

1. Eisenstein, Paul A., “NVH: The New Battleground,” Automotive Industries, Vol.174, pp.108-111, February 1994 .

2. Lord Corporation Website: http://www.lordtalent.com

3. Encarta Concise Encyclopedia Online Website: http://encarta.msn.com

4. IEEE Standard on Piezoelectricity: Std 176-1987, The Institute of Electrical andElectronics Engineers, Inc, 1988.

5. Sensor Technology Limited Website: http://www.sensortech.ca/fig1-3.html

6. Hagood, N. W. and von Flotow, A., “Damping of Structural Vibrations withPiezoelectric Materials and Passive Electrical Networks,” Journal of Sound andVibration, Vol. 146, No. 2, pp.243-268, April 1991.

7. Mulcahey, B. and Spangler, R. L., “Peizos Tame Tough Vibrations,” MachineDesign, Vol. 70, No. 4, pp. 60-63, February 1998.

8. “Batter Up! Piezo Dampers Take Sting Out of Swing,” Machine Design, Vol. 70, No.15, pp. 46-47, August 1998.

9. Sun, J.Q., Norris, M.A., Rossetti, D.J., and Highfill, J.H., “Distributed PiezoelectricActuators for Shell Interior Noise,” Transactions of the ASME Journal of Vibrationand Acoustics, Vol. 118, No.4, pp. 676-681, October 1996.

10. Shields, W., Ro, J., and Baz, A., “Control of Sound Radiation from a Plate into anAcoustic Cavity Using Active Piezoelectric-Damping Composites,” Proceedings ofthe SPIE-The International Society for Optical Engineering, Vol. 3039, pp. 70-90,1997.

11. Varadan, V.V., Wu, Z., Hong, S.Y., and Varadan, V.K, “Active Control of SoundRadiation from a Vibrating Structure,” IEEE 1991 Ultrasonics SymposiumProceedings, Vol. 1386, pp. 991-994, 1991.

12. Varadan, V.V., Gopinathan, S.V., Hun Lim Young, and Varadan, V.K., “RadiatedNoise Control via Structural Vibration Control,” Proceedings of the SPIE-TheInternational Society for Optical Engineering, Vol. 3323, pp. 546-553, 1998.

13. Lecce, L., Franco, F., Maja, B., Montouri, G., and Zandonella, N.C., “VibrationActive Control Inside a Car by Using Piezo Actuators and Sensors,” 28th

International Symposium on Automotive Technology and Automation, pp. 423-432,1995.

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14. Henrioulle, K.K., Dehandschutter, W., and Sas, P., “Increasing the SoundTransmission Loss Through a Double Panel Partition Using a Distributed AcousticActuator,” Journal-A, Vol. 39, No. 1, pp. 30-34, March 1998.

15. Xiaoqi, B., Varadan, V.V., and Varadan, V.K., “Active Control of SoundTransmission Through a Plate Using a Piezoelectric Actuator and Sensor,” SmartMaterials and Structures, Vol. 4, No. 4, pp. 231-239, December 1995.

16. Forward, R.L., “Electronic Damping of Vibrations in Optical Structures,” AppliedOptics, Vol. 18, No. 5, pp. 690-697, March 1979.

17. Davis, C.L., and Lesieutre, G.A., “A Modal Strain Energy Approach to the Predictionof Resistively Shunted Piezoceramic Damping,” Journal of Sound and Vibration, Vol.184, No. 1, pp. 129-39, 1995.

18. Edberg, D.L., Bicos, A.S., and Fechter, J.S., “On Piezoelectric Energy Conversion forElectronic Passive Damping Enhancement,” Proceedings of Damping, San Diego,CA, 1991.

19. Hollkamp, J.J., “Multimodal Passive Vibration Suppression with PiezoelectricMaterials and Resonant Shunts,” Journal of Intelligent Material Systems andStructures, Vol. 5, No. 1, pp. 49-57, January 1994.

20. Wu, S.Y., “Piezoelectric Shunts with Parallel R-L Circuits for Structural Dampingand Vibration Control,” Proceedings of the SPIE, Vol. 2720, pp. 259-269, June 1996.

21. Wu, S.Y., and Bicos, A.S., “Structural Vibration Damping Experiments UsingImproved Piezoelectric Shunts,” Proceedings of the SPIE-The International Societyfor Optical Engineering, Vol. 3045, pp. 40-50, 1997.

22. Hollkamp, J.J., and Gordon, R.W., “An Experimental Comparison of PiezoelectricConstrained Layer Damping,” Smart Materials and Structures, Vol. 5, No. 5, pp. 715-722, October 1996.

23. Ghoneim, H., “Application of the Electromechanical Surface Damping to theVibration Control of a Cantilever Plate,” Journal of Vibration and Acoustics, Vol.118, pp. 551-557, October 1996.

24. Aldrich, J.B., Hagood, N.W., von Flotow, A, and Vos, D.W., “Design of PassivePiezoelectric Damping for Space Structures,” Proceedings of the SPIE-TheInternational Society for Optical Engineering, Vol. 1917, No. 2, pp. 692-705, 1993.

25. Edberg, D.L., Bicos, A.S., “Design and Development of Passive and Active DampingConcepts for Adaptive Space Structures,” Active Materials and Adaptive Structures-

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89

Proceedings of the ADPA/AIAA/ASME/SPIE Conference, Vol. 925, pp. 377-382,1992.

26. Hollkamp, J.J., and Starchville, T.F., “A Self-Tuning Piezoelectric VibrationAbsorber,” Journal of Intelligent Material Systems and Structures, Vol. 5, pp. 559-566, July 1994.

27. Davis, C.L., Lesieutre, G.A., “An Actively-Tuned Solid State Peizoelectric VibrationAbsorber,” Proceedings of the SPIE-The International Society for OpticalEngineering, Vol. 3327, pp. 169-82, 1998,.

28. Horowitz, P. and Hill, W., The Art of Electronics, Cambridge University Press,Cambridge, pp. 281, 1989.

29. Beis, D.A., and Hansen, C.H., Engineering Noise Control: Theory and Practice,E&FN Spon, London, UK, 1996.

30. “Laboratory Measurements of the Airborne Sound Barrier Performance of Automotive Materials and Assemblies,” SAE Standards, Document Number J1400, May, 1990.

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APPENDIX AM-FILE USED FOR INITIAL SHUNT RESISTOR VALUES

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A2

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% plate.m Last edited 4/2/99%% Wnd:open circuit frequency;% Wne:short circuit frequency;% We:electric resonant frequency% K31=input('What is K31=');

Wnd=250.375Wne=249.3125K31=sqrt((Wnd^2-Wne^2)/Wne^2)%(Generalized Electromechanical Coupling Constant˝

˝disp('*** In resonant tuning case ***');˝

˝% K3t=3800; %(Relative Dielectric Constant)% epi=8.85E-12;% Area=0.07239*0.07239; %(Area of PZT)% t=2.67E-4; %(PZT Thickness)% Cpt=K3t*epi*Area/tk31=0.44;% Cps=Cpt*(1-k31^2) %(Calculated PZT Capacitance)Cps=410E-9 %(Experimental PZT Capacitance)

deltaopt=sqrt(1+K31^2) %(Optimal Tuning Ratio)ropt=sqrt(2)*(K31/(1+K31^2)) %(Optimal Damping Ratio)We=deltaopt*Wnd %(Electrical Resonant Frequency)

inductor=1/(2*pi*We)^2/Cps %(Calculated Inductor Value)

Res=ropt/(Cps*Wne*2*pi)Opres=sqrt(inductor/(4*Cps))

freq=1/sqrt(inductor*Cps);Hz=freq/(2*pi) %(Tuning Frequency)

disp('*** Shunt Resistor Value ***');r=sqrt(1-k31^2);Res1=r/(Cps*Wne*2*pi) %(Shunt Resistor Value)

disp('*** Inductor Resistor Value ***');

R135=10E3capacitor=10E-9;Rstar=inductor/capacitor;R2=R135^3/Rstar %(Inductor Resistor Value)

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APPENDIX BFINE-TUNING THE SHUNT RESISTORS WITH TESTING

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B2

FINE-TUNING THE SHUNT RESISTORS WITH TESTING

For the first iteration of testing, the shunts were initially tested without a load resistor. The

reason for this was that the internal resistance of the circuit might have been larger than the

required load resistance. The addition of a load resistor could have increased the damping level

above the desired optimum damping level. The second iteration of testing involved ‘reading’ the

results and determining whether the circuit resonance should be increased or decreased. The

technique of ‘reading’ the results will be explained here in further detail. For the third iteration of

testing, a load resistor was applied, as necessary, to adjust the damping level of the circuit.

To further explain the tuning process, the following figures demonstrate how each of the

three shunt circuits used in this study were tuned to decrease the peaks occurring around 120,

150, 240, and 260 Hz.

Shunt Circuit Tuning for the 120Hz Peak

Figure B1 shows the results from the tests required to determine the open-circuit and short-circuit

resonance frequencies, which were required to calculate the optimal electrical resonant frequency

of the circuit. The difference in resonant frequency between the two responses is about 1.25 Hz.

The required inductor resistance was then calculated to be 2307 Ω. The circuit was then tested

without a load resistor and compared to the open- and short-circuit responses, as shown in Figure

B2.

Based on these initial results, three issues were determined. The first was that the shunt

circuit was tuned to the right frequency because the shunted response is symmetric within the

short-circuited response curve. Secondly, it was determined that the internal circuit resistance

was already too high, or rather, there was already too much damping in the circuit. If there was

not enough damping there would be a dip at the resonant frequency and two peaks would occur

on either side of the resonant frequency. Thirdly, the vibration levels could not be decreased any

more with the PZT, i.e., damping ability was maximized. This was concluded because the shunt

was tuned to the right frequency, and the shunt resistance (shunt damping) was already internally

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B3

too high. Adding more resistance to the shunt would only have increased the shunted PZT plate

response.

90 95 100 105 110 115 120 125 130 135 1400

20

40

60

80

100

120

140FRF, PZT Plate Accel/Frame Accel.

Frequency, Hz

Pla

te A

ccel

/Fra

me

Acc

el,

gs/g

s

open-circuitshort-circuit

Figure B1. Open Circuit and Short Circuit Response

90 95 100 105 110 115 120 125 130 135 1400

20

40

60

80

100

120

140FRF, PZT Plate Accel/Frame Accel

Frequency, Hz

Pla

te A

cc

el/F

ram

e A

cc

el,

gs/g

s

< ---R2=2307

open-circuitshort-circuitshunt-circuit

Figure B2. Initial Results Using the Calculated Inductor Resistor Value (w/o Load Resistor)

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B4

Shunt Circuit Tuning for the 150Hz Peak

The tuning process of the shunt circuit for the 150-Hz peaks demonstrates the occurrence of

under- or over-damping using the shunt circuit. It also illustrates how the shunt circuit was tuned

to the right frequency. Figure B3 shows the initial results using the calculated inductor resistor

value without a load resistor.

130 135 140 145 150 155 160 165 1700

5

10

15

20

25

30FRF, PZT P late Acc el/Fram e Accel

Frequency , Hz

Pla

te A

cc

el/

Fra

me

Ac

ce

l, g

s/g

s

< ---R2=3630

open-circuitshort-circuitshunt-c ircuit

Figure B3. Initial Results Using the Calculated Inductor Resistor Value

(w/o Load Resistor)

Two issues were determined from these initial results: the shunt was underdamped, and the shunt

still needed more tuning to obtain the optimal frequency. The two peaks occurring in the shunt-

circuit response were due to underdamping. The energy at the tuned frequency was displaced but

not absorbed because there was not enough damping. The shunt frequency needed to be raised

about 2Hz in order for the two peaks to be properly tuned. This was accomplished by adjusting

the inductor variable resistor until the peaks were of equal height, as shown in Figure B4.

Page 106: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

B5

130 135 140 145 150 155 160 165 1700

5

10

15

20

25

30FRF, PZT P late Acc el/Fram e Accel

Frequency , Hz

Pla

te A

cc

el/

Fra

me

Ac

ce

l, g

s/g

s

< ---R2=3800

open-circuitshort-circuitshunt-c ircuit

Figure B4. Results of Adjusted Inductor Resistor Value (w/o Load Resistor)

Once the circuit was tuned such that the peaks were of equal height, the circuit was tested again

with the calculated shunt resistor as shown in Figure B5. This figure indicates that the system

became overdamped, i.e., the shunt resistance was too high.

130 135 140 145 150 155 160 165 1700

5

10

15

20

25

30FRF, PZT Plate Accel/Frame Accel

Frequency, Hz

Pla

te A

cce

l/Fra

me

Acc

el,

gs/

gs

<-----R2=3800 Rs=2355

open-circuitshort-c ircuitshunt-circuit

Figure B5. Results of Adjusted Inductor Resistor Value (w/ Calculated Load Resistor)

Page 107: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

B6

The shunt resistance was then lowered until there were two barely distinguishable peaks. It

should be noted here that the optimal shunt frequency changes as the shunt resistance changes.

Therefore, these two peaks may not be of equal height and the inductor must be adjusted slightly

again. After the inductor was adjusted such that the peaks were of equal height, the shunt load

resistance was raised just until the peaks were no longer distinguishable. This process had to be

iterated by making small adjustments to both resistors. An example of an optimal response is

shown in black in Figure B6, which illustrates overdamping, underdamping, and the optimal

response.

130 135 140 145 150 155 160 165 1700

5

10

15

20

25

30FRF, PZT P late Accel/F rame Accel

Frequency, Hz

Pla

te A

cc

el/

Fra

me

Ac

ce

l, g

s/g

s

< ------R2=3800

Rs=2355

<---R2=3800

R2=3700Rs= 350

open-c ircuitshort-circuitunder-dampedover-dampedoptimal damping

Figure B6. Results of Over-Damping, Under-Damping, and Optimal Response

Shunt-Circuit Tuning for the 240Hz and 260Hz Peak

One shunt circuit and one PZT were used to reduce the vibration and noise levels occurring at

240 Hz and 260 Hz. This was possible because both peaks were close in frequency and were both

odd modes. The PZT placed in the center of the plate was located in the center of the sections

that deformed during vibration for the modes at both frequencies. The shunt circuit was tuned to

a frequency that was between the two resonant peaks. Because of this, the shunt-circuit tuning

process was slightly different.

The plate was first tested with the PZT open- and short-circuited, as shown in Figure B7,

and the average frequency of the two resonant peaks was calculated for each case. For example,

Page 108: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

B7

the average open circuit frequency was 250.4 Hz, and the average short-circuit frequency was

249.3 Hz. These values were then used to calculate the shunt circuit resonant frequency. Figure

B8 shows the initial results using the calculated inductor resistor value without a load resistor.

210 220 230 240 250 260 270 280 2900

5

10

15

20

25

30

35

40

45

50FRF, PZT Plate Accel/Frame Accel.

Frequency, Hz

Pla

te A

cce

l/Fra

me

Acc

el,

gs/g

s

open-circuitshort-c ircuit

Figure B7. Open Circuit and Short Circuit Response

210 220 230 240 250 260 270 280 2900

5

10

15

20

25

30

35

40

45

50FRF, PZT Plate Accel/Frame Accel

Frequency, Hz

Pla

te A

cc

el/

Fra

me

Ac

ce

l, g

s/g

s

R=10,233---->

open-circuitshort-circuitshunt-circuit

Figure B8. Initial Results Using the Calculated Inductor Resistor Value (w/o Load Resistor)

Page 109: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

B8

As with tuning the 150Hz shunt-circuit, the shunt inductor resistor had to be adjusted such that

the two peaks were equal. The 240Hz peak has more energy than the 260Hz peak and therefore

requires more damping. To account for this, the shunt frequency had to be lowered. Figure B9

illustrates the adjusted shunt circuit response. The resistor value was lowered until the response

peaks were of equal height.

210 220 230 240 250 260 270 280 2900

5

10

15

20

25

30

35

40

45

50FRF, PZT Plate Accel/Frame Accel

Frequency, Hz

Pla

te A

cce

l/F

ram

e A

ccel

, gs

/gs

<---R2=8050

open-circuitshort-circuitshunt-circuit

Figure B9. Results of Adjusted Inductor Resistor Value (w/o Load Resistor)

Once the circuit was tuned such that the peaks were of equal height, the circuit was tested again

with the calculated shunt resistor, as shown in Figure B10. This figure indicates that the system

had become overdamped, i.e., the shunt resistance was too high.

The next step was to decrease the shunt load resistor until the response was minimized.

This point was reached when a further reduction or increase in the load resistor value generated a

higher response. The optimal value for this case was obtained by reducing the shunt resistor from

1398Ω to 299Ω, as shown in Figure B11.

Page 110: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

B9

210 220 230 240 250 260 270 280 2900

5

10

15

20

25

30

35

40

45

50FRF, PZT Plate Accel/Frame Accel

Frequency, Hz

Pla

te A

cce

l/F

ram

e A

cce

l, g

s/g

s

R2=8050----------->Rs=1398

open-circuitshort-circuitshunt-circuit

Figure B10. Results of Adjusted Inductor Resistor Value (w/ Calculated Load Resistor)

Figure B11. Optimal Response with Adjusted Inductor Resistor and Load Resistor Values

210 220 230 240 250 260 270 280 2900

5

10

15

20

25

30

35

40

45

50FRF, PZT Plate Accel/Frame Accel

Frequency, Hz

Pla

te A

ccel

/Fra

me

Acc

el,

gs/g

s

R2=8050----------->Rs=1398

R2=8050---->

<------------------R2=8050 Rs=299

open-circuitshort-circuitunder-dampedover-dampedoptimal damping

Page 111: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

B10

Summary

The shunt-circuit tuning techniques utilized for this study were fairly straightforward and required

a minimal number of calculations. Every resonant peak had a different behavior, and successful

tuning was largely dependent on recognizing the trends such as those explained here.

Page 112: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

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Page 114: An Experimental Evaluation of the Application of Smart Damping Materials.pdf

APPENDIX D

SAE J400 TEST WINDOW MODIFICATIONS

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D2

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D3