NASA Contractor Report 18"185"1

Evaluation of Analysis Techniques for LowFrequency Interior Noise and Vibrationof Commercial Aircraft

A. E. Landmann, H. F. Tillema, and S. E. Marshall

Boeing Commercial Airplanes

RO. Box 3707

Seattle, Washington 9812.4-2207

Contract NASI-18027

October 1989

N/ .SANational Aeronautics andSpace Administration

Langley Research CenterHampton, Virginia 23665-5225

(NASA-CF_-I61_,I) LVALUATION OF ANALYSIS

TECHNI(_UES FOR. LOW FRF_ULNCY INTEQIOR NnlSt

ANO VI_RATIqN uF C_]MMERCIAL AIRCRAFT

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This report contains comparisons of predicted and measured vibration and interior noise levels for an

aircraft, with aft mounted propeller engines. Based on these comparisons, recommendations are made

for modeling and analysis techniques for evaluation of low-frequency engine noise and vibration in the

passenger cabin. This work was conducted under NASA contract NAS1-18027 from January, 1987

through February, 1989. Work was managed by the Acoustics Division at the NASA Langley Research

Center. During 1987 work, Mr. H. Morgan was the chief of the Acoustics Division and Mr. D. G. Ste-

phens was the technical monitor for the contract. During the 1988 and early 1989 work, Mr. D. G. Ste-

phens was chief of the Acoustics Division at NASA and Dr. K. Shepherd was the technical monitor for

the contract.

All analytical work was performed under the direction of the Noise Research staff of the Boeing Com-

mercial Airplanes. A number of engineering organizations and subcontractors contributed to the

successful completion of the project as planned. Key contractor personnel responsible for this effort

were

Noise Technolo_,

L. M. Butzel

L. W. Craig

C. G. HocJgeA. E. Landmann

S. E. Marshall

G. K. Oueitzsch

P. M. Serati

Slructures Technolo_

K. H. Dickenson

R. L. Dreisbach

R. R. EnsmingerM. T. Hutchinson

H. J. Jamshidiat

E. E. MeyerH. E Tillema

Propulsion Technolotw.M. A. Heidari

R. L. Martin

J. L. White

T. E Yantis

Weights Technolo_D. E. Cook

D. J. Roberts

Subcontractors

A. C. Aubert - Cambridge Collaborative, Inc.

J. E. Manning - Cambridge Collaborative, Inc.

L. D. Pope

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TABLE OF CONTENTS

FOREWORD ........................................................................... i

TABLE OF CONTENTS ................................................................ iii

LIST OF TABLES ....................................................................... v

LIST OF FIGURES .................................................................... vii

1.0 SUMMARY ....................................................................... 1

2.0 INTRODUCTION ................................................................. 3

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3.0

4.0

APPROACH ...................................................................... 5

3.1 Noise and Vibration Tests ..................................................... 5

3.2 Analysis Model Development .................................................. 73.2.1 Finite Element Model ................................................. 8

3.2.2 Statistical Energy Analysis Model ....................................... 93.2.3 PAIN Model ......................................................... 13

RESULTS

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

4.11

4.12

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Finite Element Analysis Results CFY 1987) ..................................... 15

Finite Element Model Improvements (FY 1988) ................................. 20

Finite Element Analysis Results (FY 1988) ..................................... 22

Statistical Energy Analysis Results (FY 1987) ................................... 33

Review of SEA Procedures for Low-Frequency Problems ........................ 38

4.5.1 Acoustic Space Modal Density Estimate ................................ 38

4.5.2 Structure Modal Density Estimates .................................... 39

4.5.3 Use of Finite Element Models to Verify SEA Parameters ................. 39

SEAM TM Code Improvements ................................................ 41

SEA Low-Frequency Model Improvements ..................................... 43

4.7.1 Input Power Estimate ................................................. 43

4.7.2 Modal Density Estimates ............................................. 44

4.7.3 Strut Connection Modeling ............................................ 44

4.7.4 Strut Loss Factor .................................................... 46

Midfrequency Model Improvements ........................................... 47

Statistical Energy Analysis Results (FY 1988) ................................... 49

PAIN Analysis Resu]ts (FY 1987) .............................................. 55

PAIN Analysis Results (FY 1988) .............................................. 57

PAIN Improvements and Feasibility Studies ..................................... 62

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5.0

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CONCLUSIONS AND RECOMMENDATIONS ..................................... 65

5.1 Finite Element Analysis ....................................................... 65

5.2 Statistical Energy Analysis .................................................... 66

5.3 PAIN Analysis ............................................................... 66

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Table

LIST OF TABLES

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727 Demonstrator Airplane Ground Vibration Test (GVT) Shake Conditions ..... 5

727 Demonstrator Airplane Flight Conditions ................................. 7

Modeling Time and Cost Comparison for 727 Demonstrator Airplane FiniteElement Models .......................................................... 33

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LIST OF" FIGURES

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Prediction Program Comparisons and Comments ............................. 1

727 Demonstrator Airplane--General Arrangement ........................... 6

BS 1010 Microphone and Accelerometer Locations ............................ 7

727 Demonstrator Airplane--Finite Element Model Finite Element Method ...... 8

GE36 Demonstrator Engine Finite Element Model ........................... 10

25-Element Low-Frequency SEAM TM Model (20- to 100-Hz Range) ............ 11

100-Element Midfrequency SEAM TM Model (100-to 400-Hz Range) ............ 12

Propeller Aircraft Interior Noise Model ..................................... 14

727 Demonstrator Airplane Predicted Versus Measured Frame Mode

Shape at BS 1010--21.5 Hz ................................................ 15

727 Demonstrator Airplane GVT--Roving Microphone Data .................. 16

727 Demonstrator Airplane GVT Accelerometer Data Frame Versus

Ceiling Panel Response at Stringer 4 ........................................ 17

Finite Element Prediction Versus 727/GE36 Demonstrator Test;

GVT--Front Mount Vertical Shake ......................................... 18

Finite Element Prediction Versus 727/GE36 Demonstrator Test;

GVT--A.ft Lower Mount Lateral Shake ..................................... 20

Original and Revised Ceiling Panel Weight Distribution ....................... 21

Original and Revised Hat Rack Weight Distribution .......................... 21

Acoustic Mesh Typical Cross Section ....................................... 23

727 Demonstrator Airplane--Reduced Finite Element Models ................. 24

Finite Element Prediction Versus 727/GE36 Demonstrator Test;

Ground Vibration Test--Front Mount Vertical Shake ......................... 25

Longitudinal Variations Around BS 1010--GE Side Window Seat

Microphone Prediction .................................................... 26

Finite Element Prediction Versus 727/GE36 Demonstrator Test;

Ground Vibration Test--Aft Lower Mount Lateral Shake ..................... 27

Finite Element Predictions Versus 727/GE36 Demonstrator Test;

Ground Vibration Test--Front Mount Vertical Shake ......................... 28

Finite Element Predictions Versus 727/GE36 Demonstrator Test;

Ground Vibration Test--Aft Lower Mount Fore-Aft Shake .................... 29

Finite Element Predictions Versus 727/GE36 Demonstrator Test;

Ground Vibration Test--Aft Lower Mount Vertical Shake ..................... 30

Finite Element Predictions Versus 727/GE36 Demonstrator Test;

Ground Vibration Test--Aft Lower Mount Lateral Shake ..................... 32

SEA2kfr,_ Predicted Levels Versus 727 Demonstrator Test Data:

GVT--Forward Mount Lateral Shake ....................................... 34

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Low-Frequency SEAM TM Model Predicted Levels Versus 727 Demonstrator

Test Data; GVT--Forward Mount Vertical Shake ............................. 35

Midfrequency SEAM TM Model Predicted Levels Versus 727 Demonstrator

Test Data; GVT--Forward Mount Vertical Shake ............................. 37

Asymptotic Modal Densities for the Low-Frequency SEA Model ............... 40

Input Power Comparisons .................................................. 42

Response Predictions for the Low-Frequency Baseline Model

Using Measured Input Power--Vertical Shake ................................ 43

Composite Strut Modal Density Based on Spacing Between Peaksin the Measured Vertical Shake Input Power ................................... 45

Instantaneous Modal Density for the Cabin Acoustic Space .................... 46

Comparison of Modal Density Prediction Procedures--Interior

Acoustic Space ............................................................ 47

Midfrequency SEAM Model Variable Panel Density ........................... 48

Response Predictions for the Low-Frequency Improved Model--Vertical Shake ............................................................ 50

Response Predictions for the Low-Frequency Improved Model

Using Measured Input Power Vertical Shake ................................. 51

Response Predictions for the Low-Frequency Improved Model--Fore-Aft Shake ............................................................ 52

Response Predictions for the Low-Frequency Improved Model

Using Measured Input Power Fore-Aft Shake ................................. 53

Response Predictions, Midfrequency Model Side-of-Body Shake,

Improved Model .......................................................... 54

Measured Minus Predicted SPL Using Impi'oved Midfrequency Model .......... 55

Power Flow Diagram for Elements of PAINUDF Model ....................... 56

Measured Versus PAINUDF Predicted Levels ................................ 57

Average of Seat Measurements Versus PAINUDF Space Average Prediction ..... 58

Propeller Wavefronts for Blade Downsweep (Forward Rotor) and Blade

Upsweep (Aft Rotor) at _ = 105 ° 59

Propeller Wavefronts for Blade Downsweep (Forward Rotor) and Blade

Upsweep (Aft Rotor) at O _ 800 59

Measured and PAINUDF Predicted Levels for Open Panel and

Conical Empennage Models ................................................. 60Measured and PAINUDF Predicted Levels Phase Sensitivity Study ............. 60

Comparison of Propeller Field Phase Contours ANOPP Phase Versus

Dummy Phase ..... ., ---,. ,.. .... . ............. . .......................... 61Measured and PAINUDF Predicted Levels PAINUDF Sensitivity

Study to Excitation Models (Mach -- 0.80 at 35 000 ft) ........................ 62

Example of Sidewall Layer Configurations ................................... 63

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1.0 SUMMARY

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This document summarizes a 2-year effort to evaluate the application of selected analysis techniques to

low-frequency cabin noise associated with advanced propeller engine installations. Work was funded by

a NASA contract, NAS1-18027.

Three design analysis techniques were chosen for evaluation including finite element analysis, statistical

energy analysis (SEA), and a power flow method using elements of SEA (computer program Propeller

Aircraft Interior Noise (PAIN)). An overview of the three procedures is provided in figure 1. Data from

tests of a 727 airplane (modified to accept a propeller engine) were used to compare with predictions.

Comparisons of predicted and measured levels at the end of the first year's effort showed reasonable

agreement leading to the conclusion that each technique had value for propeller engine noise predictions

on large commercial transports. However, variations in agreement were large enough to remain cautious

and led to recommendations for further work with each technique. This recommended work was accom-

plished in the second year's effort.

Assessment of the second year's results leads to the conclusion that the selected techniques can accu-

rately predict trends and can be useful to a designer, but that absolute level predictions remain unreli-

able due to complexity of the aircraft structure and low modal densities. The extremely complex nature

of the modified 727 demonstrator airplane may be largely responsible for this conclusion. It would be

worthwhile to apply these techniques to more conventional aircraft structure cases.

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Frequency range

(this study)

Calculations

Advantages

Disadvantages

Use

FEM

Rotor

Modes, display, SPL

versus position and

frequency

Good detail versus

frequency, position

Expensive, hard

to change model

Detailed predictions

design work for

exi_ng or new

airplanes

SEAM

Low-frequency model High-frequency model

Rotor and rotor Rotor harmonics and BPF

harmonics ( < 100 Hz)

Power, modal densities coupling loss

factors, space average display and SPL

Inexpensive/quick model

changes/power flow analysis/variance estimates

Lack of spatial details/highestimate vadance for low modal

density cases

Power flow analysis for existing

airplanes

Preliminary design

PAIN

BPF

Power structural modes

space average SPL

Moderate exp

Good trim definition

lack of spatial details,excitation field

complexity

Preliminan/design

Figure 1. Prediction Program Comparisons and CommentsUgO 196RI-4

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2.0 INTRODUCTION

The primary sources of cabin noise on advanced propeller-powered aircraft are low- to mid-frequency

(i.e., below 500 Hz) structure borne noise (caused by engine unbalances) and engine-radiated propeller

tones. Conventional sound proofing treatments, such as damping tapes or fiberglass blankets, are not

very effective in this frequency range. Also, most low- to mid-frequency design tools tend to be based on

idealized cylindrical models of the aircraft fuselage, which ignore effects of tapered empennage sections,

pressure bulkheads, floors, etc. Effective reduction of low- to mid-frequency noise requires the develop-

ment of improved design analysis tools. These improved tools will lead to a better understanding of the

mechanisms involved and provide guidance for developing new suppression concepts.

The objective of the FY 1987 task under contract NAS 1-18027 was to evaluate the ability of three analysis

techniques (contained in existing computer programs) to predict cabin noise and vibration. Specific

steps of this effort were as follows:

1. Predict cabin noise, together with vibration levels of the floor, cabin sidewall, pressure bulkhead,

empennage, and strut at rotor (once per revolution) and propeller-blade-passage frequencies.

. Compare predicted levels with measured levels from a 727 demonstrator aircraft modified to accept

a GE36 counter-rotating propeller engine. Make predictions and comparisons for ground vibration

test and inflight conditions.

3. Determine strengths and shortcomings of prediction program procedures and/or modeling tech-

niques and identify potential means for improvements.

The objectives of the FY 1988 task were to incorporate recommended improvements, repredict noise

and vibration levels, compare the new predictions to measured levels, assess results, and make recom-

mendations for future use of these procedures.

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3.0 APPROACH

While the NASA contract focused on predictions and comparisons with test data, preliminary work

including 727 test descriptions and analysis model development is also included in this report.

3.1 NOISE AND VIBRATION TESTS

Noise and vibration testing on a 727 aircraft, modified for installation of a GE36 counter-rotating pro-

peller engine, provided the database with which to compare predictions. During ground vibration tests,

before engine installation, the strut was excited by a shaker to determine airframe and cabin response to

engine mount vibration. Response to shaker inputs at each engine mount location was recorded. In addi-

tion, side-of-body shake testing was performed on the fin, empennage, and aft passenger cabin to simu-

late high-level acoustic loading from the propellers. Ground vibration test conditions are given in table 1.

The 727 was configured with an acoustic test arena aft of body station 890. Standard 727 interior trim

and four passenger seat rows were installed in this area. General layout of the aircraft is shown in

figure 2.

Instrumentation locations were reviewed to ensure adequate data for comparison with predicted levels.

Cabin microphones were placed in the acoustic arena to monitor noise at passenger seated and standing

locations as well as next to interior vibration sensors (fig. 3). Also shown are accelerometers positioned in

the passenger cabin to monitor fuselage sidewall, floor, and cabin interior trim response.

Accelerometers were placed on the pressure bulkhead, empennage, and strut to evaluate the transmis-

sion path to the passenger cabin. A total of 128 response channels were measured for each ground vibra-

tion test condition.

Due to data channel limitations during flight testing, fuselage and cabin accelerometer numbers were

reduced. Further reductions were required to add flush mounted exterior microphones for the purpose

of measuring propeller noise excitation levels. Different cruise and low-power flight conditions were

completed (table 2).

Table 1. 727 Demonstrator Airplane Ground Vibration Test (GVT) Shake Conditions

Side-of-body shakes, 10 to 400 Hz Engine mount shakes, 2 to 200 Hz

BS 1160 WL 320

BS 1270 WL 190

BS 1300 WL 250

BS 1310 WL 340

B,S1400 WL 400

BS 1050 WL 23O

Front mount vertical

Front mount lateral

Aft upper mount vefdcal

Aft upper mount lateral

Aft upper mount fore to aftAft lower mount vertical

Aft lower mount lateral

Aft lower mount fore to aft

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Table 2. 727 Demonstrator Airplane Flight Conditions

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3.2 ANALYSIS MODEL DE .VELOPMENT

Three design analysis techniques were chosen for evaluation including finite element analysis, statistical

energy, analysis (SEA), and a power flow method using elements of SEA (computer program PAIN). An

existing general application SEA computer program, SEAM TM, was chosen for evaluation based in part

on past successful applications to helicopter, ship, and automobile problems. The developer of

SEAM TM, Cambridge Collaborative, Inc., was retained as a subcontractor for this effort. Computer

7

program PAIN was specifically developed for propeller interior noise predictions. L. D. Pope, a co-

author of PAIN was also retained as a subcontractor.

3.2.1 FINITE ELEMENT MODEL

As a starting point for finite element analysis, an existing 727 aircraft finite element model suitable for

loads analysis was selected. Changes to model the modified structure (to accommodate the propeller

engine), the mass of the interior trim and systems, and an interior cabin acoustic volume were then incor-

porated. The model is shown in figure 4. Detailed finite element models of the fuselage containing the

acoustic arena and structural elements along the transmission path, such as the pressure bulkhead, em-

pennage, vertical fin, and strut, were used. In the fuselage section, body frames, floor beams, stringers,

and skin were all individually modeled. Body frames and floor beams were represented as beams, string-

ers as rods, and skin as membrane plates. In the test arena section, nodes were located at each frame and

Horizontal tailbeam model

STA 1183IIBq B

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mass (typicaT)_ Detailed stiffness and mass

model of the aft fuselage

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Figure 4. 727 Demonstrator Airp/ane-Finite E/ement Mode/Finite E/ement Method

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stringer intersection. Nodes of the cabin acoustic model interfaced with existing sidewall, floor, and

bulkhead structural nodes.

The model was completed by including beam models of the forward fuselage, wings, and horizontal tail.

The complete aircraft model was generated because the contribution of gross airplane modes to trans-

mission of low-frequency rotor noise was unknown, but potentially important.

Due to model size and existing node spacing, it was decided to limit predictions to the rotor frequency

range. The fuselage nodes were at each frame and stringer intersection, which would have been too

coarse a grid to predict skin panel modes that occur in the propeller-blade-passage frequency range

(-200 Hz). Because no dynamic nodes of the interior trim were expected below 30 Hz, the interior trim

was modeled by lumped mass only. Seat absorption was expected to be minimal below 30 Hz; therefore,

seats were also represented by lumped mass only. Additional tap tests of interior trim surfaces and rov-

ing microphone measurements were made around seats to validate these assumptions.

For inflight calculations, an engine model was also developed consisting of a beam element representa-

tion of the core engine and a shell model of the propulsion section (fig. 5).

Predictions using this model were made for unit force inputs and compared to measured ground vibra-

tion test (GVT) and flight transfer functions.

3.2.2 STATISTICAL ENERGY ANALYSIS MODEL

The primary task within the SEA procedure is to formulate power balance expressions for the substruc-

tures (energy storing mode groups) of the model. The substructures are typically simple representations

(e.g., plates, beams, and acoustic volumes) for sections of the modeled system. Physical information de-

scribing the system is used to define the substructure properties such as modal density (the average

number of resonances per unit frequency), characteristic wave number (a quantity directly related to the

average wavelength of a mode), characteristic impedance (the ratio of the maximum force to the maxi-

mum velocity for a mode of vibration), and coupling loss factor (a parameter controlling the average flow

of energy between two groups of modes). The power expressions are then solved for the modal energies

within the substructures. From the modal energies, the response variables of interest for the specified

substructures are determined. The input excitation for a SEA model is applied as the power input to a

subsystem of modes.

Because of the smaller model size requirements for SEA, it was decided to use this technique to predict

levels for both the rotor and propeller-blade-passage frequency ranges. The first model developed as

part of the SEA effort was intended to predict the structural and acoustic response near the propeller

tone frequency (100- to 400-Hz frequency range). This model consisted of approximately 400 SEAM TM

type subsystems and more than 2000 junctions, which, up to this point, was the largest SEAM TM model

developed by Cambridge Collaborative. This model contained elements representing the composite

bending and inplane activity of frame and stringer stiffened structure, elements that represented skin

panels without stiffeners (bending and inplane), trim elements, cabin acoustic space elements, and

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acoustic elements that represented the space between the fuselage sidewall and trim panel. Initial pre-

dictions with this model indicated good agreement at the drive point, but overprediction at points away

from the drive point. Cambridge Collaborative concluded that the inability of the model to predict the

measured rolloff in response was due to the inclusion of inplane subsystems in the model, which lead to

overcoupling between subsystems.

In addition, it was found that the small element sizes resulted in modal densities that were too low based

on Cambridge Collaborative's past experience. As a result of these efforts, new models for rotor and

propeller tone predictions were generated (figs. 6 and 7) using larger substructure elements and elimi-

nating inplane activity. Data from manufacturing drawings were used to generate separate models in

each frequency range using basic pipe, plate beam, and airspace elements available in SEAM TM.

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Figure 6.

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The low-frequency model was developed to predict the interior acoustic response to mechanical excita-

tion of the engine strut. The transmission of vibration from the unducted fan (UDF) engine caused by

fan rotor imbalance was expected to dominate cabin noise within the low-frequency range (20 to 100 Hz).

As with the finite element model, the low-frequency SEA model (for rotor frequencies) did not account

for cabin trim or seats (other than mass). The substructure elements shown in figure 6 were selected

based on natural boundaries between areas of different structural properties or construction. Rather

than the detailed finite element modeling of skin, stringers, and frames, composite bending stiffnesses of

the plate or pipe elements were calculated to include the effects of the aircraft structural elements as

described below.

The material properties required for the SEA model are density., longitudinal wavespeed, shear wa-

vespeed, and damping loss factor. The substructures used in the low-frequency model consist of

composite bending modes. Effective material properties for these substructures were obtained from a

composite bending calculation that includes the mass and stiffness of frames and stringers and the mass

of fuselage sidewall trim panels. The properties and thickness of a homogeneous structure were set to

obtain the same bending wavespeed and surface density. Two approaches can be used: (1) an equivalent

material density approach (or stiffness thickness approach) in which the thickness of the structure is

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modified to give the correct bending wavespeed and the density is modified to give the correct density

per unit area and (2) an equivalent material density approach (or mass thickness approach)in which the

thickness of the structure is modified to give the correct density per unit area and the longitudinal wa-

vespeed is modified to give the correct bending wavespeed. For the low-frequency model the equivalent

material density approach was used for all shell or pipe substructures and the equivalent wavespeed

approach was used for plate structures. Use of the equivalent material density approach for shell or pipe

substructures allowed the longitudinal wavespeed to be held constant so that the ring frequency of the

substructure was unchanged.

I

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I

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i

The mid-frequency SEA model (for propeller frequencies-fig. 7) differed from the low-frequency model

in substructure element size, composition, and handling of the trim and seats. The substructure element

boundaries were chosen to reflect finer variations in construction (both axially and eircumferentially)

that were felt might effect response in this frequency range. Composite bending stiffnesses as well as skin

membrane stiffnesses were included in the fuselage plate elements. Because independent dynamic

modes of the interior trim were expected in this frequency range, the trim was modeled separately as

plates. Acoustic spaces between the skin and trim panels were also included. The effect of seats was

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included by separately modeling acoustic volumes above and below seatback levels. Coupling between

acoustic volumes below seatback level was adjusted to account for seat blockage. Material properties

were generated in the same fashion as for the low-frequency model.

Model predictions for both cases were again made for unit force inputs and compared to measured GVT

and flight transfer functions.

3.2.3 PAIN MODEL

The Propeller Aircraft Interior Noise (PAIN) prediction method (theory and computer implementation)

was previously developed by L. D. Pope, et al., under the auspices of NASA. The PAIN model estimates

the space average sound level in an airplane cabin resulting from an excitation field incident on the exte-

rior fuselage (fig. 8A). The excitation field consists of the pressure time history for a wing-mounted rotat-

ing propeller as defined by a grid of points on the fuselage surface.

The computer program PAIN was used to predict inflight cabin noise levels at the propeller-blade-

passage frequency. As mentioned above, PAIN was originally developed for general aviation aircraft

with wing-mounted propeller engines. In this form, only one uniform fuselage structural description was

allowed. In contrast, the 727 demonstrator aircraft had an aft fuselage-mounted propeller engine, and

most of the propeller tone noise fell on the empennage rather than the passenger cabin fuselage. There-

fore, before PAIN could be used, a significant modification for 727 predictions was completed by refor-

mulating the problem to allow representation of both the passenger cabin fuselage and empennage

structures (fig. 8B). The 727 demonstrator airplane empennage consists of a very stiff sidewall supported

by torque boxes at the top and bottom. To model this behavior, the empennage was represented by open,

curved panels.

The capability to model both fuselage and empennage structures is contained in computer program

Propeller Aircraft Interior Noise Unducted Fan (PAINUDF). The empennage element allows for the

region on which the excitation field acts to differ in both construction and location from the fuselage

region inside which cabin noise estimates are desired. Additionally, a junction between the two regions is

defined by a structurally significant (but nonacoustically radiating) bulkhead.

With PAIN, the fuselage sidewall is modeled in a simpler manner than with finite element modeling. The

sidewall was represented as a cylinder with an equivalent skin thickness based on skin dimensions and

smeared frame and stringer properties. The floor was modeled in a similar manner. The interior trim

was modeled as an airgap with absorption and a limp mass trim. The interior airspace was modeled as

one uniform volume. Data from manufacturing drawings were used to determine equivalent skin and

floor panel thicknesses, insulation properties, and trim mass.

Data from flush-mounted microphones were then used to describe excitation forces, allowing inflight aft

cabin noise level predictions to be made. Changes to the computer code as well as predictions and com-

parisons were made under the NASA contract.

13

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(b) 727/GE36 Demonstrator Airplane PAIN Mode/

Figure 8. Propeller Aircraft Interior Noise Mode/

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4.0 RESULTS

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4.1 FINITE ELEMENT ANALYSIS RESULTS (FY 1987)

Predictions were made to encompass the rotor frequency range ( < 30 Hz) and were compared to GVT

and flight test conditions. A modal solution was used, meaning a limited number of structural and

acoustic modes were computed and used to generate forced response predictions. In this case, 150 struc-

tural modes (0 to 73 Hz) and 100 acoustic modes (0 to 230 Hz) were used.

Inspection of predicted mode shapes showed gross airplane modes involving the wings, tail, and fuselage

from 0 to 30 Hz; local frame and floor bending modes occurred above 20 Hz. Comparison with test data

showed good agreement. Below 20 Hz, predicted gross airplane mode shapes matched results from mea-

sured data, with predicted resonant frequencies typically within 5% of those measured. From 20 to 30

Hz, fuselage modes occur in which the frame exhibits a maximum of three half-waves around the passen-

ger cabin and the floor one half-wave across the cabin. Measured data showed similar response charac-

teristics (fig. 9). The measured data in figure 9 includes both frame and floor bending plus rigid body

translation associated with gross airframe bending. Since only radial accelerometers were used during

testing, the local bending and rigid translation responses could not be separated. It was recommended

that future rotor frequency shake tests use biaxial accelerometers. A few modes related to strut response

Prediction Test

a

21.501 Hz 21.48 Hz

Figure 9. 727 Demonstrator Airplane Predicted Versus Measured Frame ModeShape at BS 1010-21.5 Hz

UgO196RI-14

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were also identified, but either did not appear in measured data or were shifted in frequency by a signifi-

cant amount. The cause of these modes was investigated as part of the FY 1988 task.

One cabin acoustic mode was predicted in the frequency range below 30 Hz. At 23 Hz a longitudinal

mode was predicted and represented by a standing half-wave between the pressure bulkhead and a par-

tition at body station 890 used to separate the test arena from the rest of the airplane. Cross-cabin modes

occurred at more than 50 Hz.

As stated in the Approach section, additional tests were performed to validate seat and trim modeling

assumptions for the rotor frequency range. Noise measurements made at several locations around one

seat during a body shake condition showed only small variations at less than 50 Hz (fig. 10). Trim and

ceiling panel tap tests showed no modes in the rotor frequency range. Shake test data showed that the

ceiling panel followed the primary structure response to slightly more than 30 Hz (fig. 11).

Example comparisons of test with analysis for the strut, pressure bulkhead, fuselage sidewall, floor, and

acoustic space are given in figures 12A through 12F for one GVT condition. Predicted peak levels fell

SLP, dB

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9-Ug_196Rl-16

within 10 dB of the measured levels with frequency shifts up to 1.5 Hz. It was felt that agreement could be

improved with the additional modeling studies and recommendations discussed below.

Figure 12A compares measured and predicted strut response for the vertical strut shake condition. Gen-

erally, levels were overpredicted at less than 19 Hz and underpredicted at more than 19 Hz. The mode

predicted at 14.5 Hz and shown shifted in the test data to near 16 Hz illustrates some of the questions

about strut modeling that were recommended for investigation.

Figure 12B shows radial response of a stringer at the intersection of the fo_'ard strut spar and the pres-

sure bulkhead. Agreement was very good although the trend of overprediction at low frequencies and

17

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Finite Element Prediction Versus 727/GE36 Demonstrator Test;GVT-Front Mount Vertical Shake

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underprediction at higher frequencies seen in the strut response was repeated. The drop out at 22.5 Hz

appeared to be related to a spurious strut mode.

Figure 12C compares predicted and measured pressure bulkhead response. Predicted levels were very

close to test with a 1.5-Hz shift in frequency believed to be related to the above noted strut modes.

Figures 12D, E, and F show body frame, floor, and acoustic response comparisons at body station 1010,

approximately the middle of the test arena. While comparisons are reasonable, some of the largest varia-

tions between prediction and test were noted at floor and frame locations. Also, the differences varied

considerably between individual measurement points. It was believed that inappropriate lumping of in-

terior masses might have shifted the predicted locations of modal node points, which could have a sub-

stantial effect when comparing individual points. At the beginning of the modeling effort, it was assumed

that the interior trim mass could be uniformly spread. From these results, it appeared that this assump-

tion was not valid. Interior trim and seats are in fact mounted at discrete locations with the baggage

racks and seats being cantilevered from the frames and floor beams. It was recommended that sensitivity

studies of mass representation and distribution be completed using the 727 demonstrator airplane mod-

el to define mass loading representation requirements.

Figure 12F compares predicted and measured noise levels at a passenger seat. The major trends were

predicted and good agreement at the peak response point (for the half-wave axial mode) was observed. It

was noted, however, that the predicted response peak was sharper and shifted to a higher frequency than

the data. A partition located at body station 890 to separate the test arena from the rest of the airplane

was assumed to be rigid for modeling purposes. Inspection of the data suggested that the partition was

providing some low-frequency absorption in the form of mechanical vibration. This tended to broaden

peak response and shift it to a lower frequency as seen in the test data.

In the initial finite element model, only the cabin airspace was represented. Previous analysis on simpli-

fied fuselage section models indicated that the cargo compartment airspace could have a significant

effect on passenger cabin acoustic response, particularly at acoustic resonances. It was recommended

that this be included in the full 727 demonstrator airplane model.

Comparisons of predicted and measured levels for other shake conditions generally led to the same con-

clusions as the vertical shake condition with the following one exception. For shake directions in the

plane of the strut, a predicted strut mode at 23 Hz coupled with the cabin acoustic mode at the same

frequency resulted in an overprediction of interior noise levels. Measured data showed a similar strut

mode with lower response near 28 Hz (fig. 13A). The resulting overprediction in noise is shown in figure

13B. Another factor possibly contributing to the overprediction at the acoustic resonance was the rigid

boundary condition assumed for the acoustic curtain.

Flight data predictions did not match well with measured levels. The model showed a great deal of sensi-

tivity to both input unbalance levels and phase between propellers. Unfortunately, measured response

data did not include phase information referenced to the propellers that made assessment of flight

19

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Legend:..... Gv'r data

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(e) Aft Lower Engine Mount Lateral Response

Legend:..... GVT data......... FEM prediction

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(b) BS 1010 Loft Side Aisle Seat Microphone

Figure 13. Finite Element Prediction Versus 727/GE36 Demonstrator Test;GVT-Aft Lower Mount Lateral Shake

E)-UgO106R1-18

predictions difficult. Phase measurements referenced to propellers were recommended for any future

testing.

Agreement between predicted and GVT data showed the finite element modeling procedure to be a

valid tool for predicting low-frequency structural-acoustic behavior. Based on the above results, it was

recommended that studies of strut and acoustic curtain modeling and trim mass distribution be

completed.

Use of the finite element model was found to be time consuming and expensive. The sheer size of the

model made assembly and checkout a very lengthy process. Turnaround of results was also slow. It was

also recommended to systematically reduce the size and simplify the model to define the minimum mod-

el size requirements versus frequency. As stated previously, the entire aircraft was modeled because the

effect of gross airplane modes was not known.

4.2 FINITE ELEMENT MODEL IMPROVEMENTS (FY 1988)

The existing finite element model was refined by improving the mass distribution of interior nonstruc-

tural elements and improving the acoustic curtain representation. The propeller engine strut model was

checked for modeling errors due to spurious modes identified during 1987 work. Some errors were found

and corrected. Details are given below.

The initial finite element modeling procedure simply smeared the mass of interior trim and seats evenly

as shown for a ceiling panel example in figure 14A. In fact, this panel is supported only at discrete points

along its edges. The mass of the ceiling panel was redefined as concentrated masses at the attachment

points only (fig. 14B). The hat rack and seats were originally defined as lumped masses at the fuselage

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mold line and in the plane of the floor, respectively. Their masses were redefined as concentrated masses

located at the center of gravity. The hat rack change is portrayed in figure 15.

The test airplane configuration included a partition to separate the forward portion of the aircraft, which

was filled with test equipment from the aft acoustic test arena. This partition was constructed from a

honeycomb board with fiberglass and lead vinyl installed on both sides. Original modeling assumed this

S-1 S-1

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Figure 15. Original and Revised Hat Rack Weight DistributionUgO196R1-20

21

D

partition to be rigid, Predicted acoustic response showed the acoustic resonance to be 1 to 2 Hz more

than seen in the test. This may be the result of ignoring the effects of mechanical vibration in the initial

model. Therefore, the acoustic partition model was changed to a flexible partition using brick elements

to represent the mass and stiffness of the fiberglass and lead vinyl septum on the test arena side.

It was noted previously that strut modes were predicted that either did not occur ifi the measured results

or were at significantly different frequencies. It was suspected that the strut and empennage connection,

very complex for the modified demonstrator aircraft, might be in error. The model was compared to

drawings and a few changes were made with the net effect of increasing strut stiffness.

The above changes constituted the improved finite element model that was used to repredict ground

vibration test conditions. In addition, further studies were conducted by representing the cargo com-

partment airspace and by systematically reducing the size of the improved model. A finite element mesh

of the cargo compartment airspace was generated that interfaced with the lower sidewall and floor

structural nodes. The cabin acoustic model interfaced with the same floor nodes allowing coupling be-

tween the acoustic spaces (fig. 16).

As was noted previously, the size of the finite element model made its use time consuming and expensive.

Figure 17 shows model representations that were studied to define minimum model size requirements.

In the first case, the stiffness and mass substructures aft of BS 1183 were dynamically reduced to the

retained degrees of freedom at the aft pressure bulkhead and the engine attach points. In the second

case, the empennage and tail section aft of the strut rear spar were replaced by a beam model. Finally, a

representation that ignored structure aft of the strut rear spar and forward of the acoustic test arena wasconsidered.

4.3 FINITE ELEMENT ANALYSIS RESULTS (FY 1988)

Predictions made using the refined baseline model are given in figures 18 through 24. Figures 18 and 20

compare 1987 and 1988 predictions to GVT data. In this case, results are plotted up to 40 Hz in order to

better understand response characteristics around 30 Hz. Overall, the refined finite element model

yields reasonable predictions of the GVT response. The most notable improvement in predictions asso-

ciated with this model is the acoustic response at the acoustic resonance for lateral and axial shake

conditions.

Figure 18 compares predictions to test for a front mount vertical shake condition at several of the posi-

tions discussed previously. At the drive point (fig. 18A) the new prediction follows the trends seen in the

GV'E As a direct result of the improved strut and bulkhead modeling, a closer match of prediction and

test is obtained at less than 24 Hz. At more than 24 Hz, the model still underpredicts the data.

Figures 18B, C, and D show body frame, floor, and acoustic response comparisons at approximately the

middle of the test arena (BS 1010). It was this area that was noted to have some of the largest variations

between prediction and test when evaluating 1987 results. This led to the review and improvement of the

interior trim mass distribution in the refined model. Although the refined model yieIds reasonable

22

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predictions of trends and levels, there is no clear improvement over 1987 results. In fact, the response

prediction for the window seat microphone appears worse. However, at this frequency the model is very

sensitive to axial position because of the node line of the first acoustic mode. Changing the acoustic

partition properties has moved the predicted response node position slightly. Figure 19 compares the

predicted noise levels at three sequential axial positions near the GVT measurement point. As can be

seen, there is a 20 dB difference at approximately 22 Hz in the three predictions with the prediction for

BS 990 closely matching the data at BS 1010. This illustrates one of the difficulties in comparing the test

data to prediction on a point-to-point basis.

23

d

|Reduced model A- Reduced model B- Reduoed model C-

dynamic reduc_on of aft-end shell structure aft-end beam model passenger cabin and strut model

Figure 17. 727 Demonstrator A/rp/ane-- Reduced Fin�re E/ement Mode/sg,UQO106RI-22

For the lateral shake condition, the refined model did a better job than the original model based on

improvements to the strut and acoustic curtain models. At the drive point, the predicted response

follows the measured response trend at less than 24 Hz (fig. 20A). The refined model now predicts a

mode at 24.5 Hz (versus 23 Hz originally) that corresponds to a 28-Hz peak in the measured data. Simi-

larly, a 37-Hz peak in the measured data is also underpredicted by approximately 3 Hz. This

improvement in strut response prediction coupled with the more accurate representation of the acoustic

curtain led to a much improved prediction for the interior noise level (fig. 20B).

As stated earlier, point-to-point comparisons of test data and prediction can be difficult due to uncer-

tainties associated with exact location of test instrumentation and small differences in location between

predicted and measured modal node lines. An alternate way to assess the finite element model predic-

tions is to compare the range of response for all individual measurements of a common set of instrumen-

tation with the corresponding predicted levels. Figures 21 and 22 compare measured ranges of test data

to predictions for the front mount vertical shake and aft lower mount fore-aft shake conditions,

respectively. The areas shown for comparison are the bulkhead, the floor, the body frame at BS 1010, and

the cabin interior.

For the front mount vertical shake condition, the majority of predictions for the individual locations fall

within the range of measured data with the exception of the floor response. Predictions are particularly

good at more than 20 Hz. For comparison, data and predictions for an aft mount fore-aft shake condi-

tion are presented in figure 22. The same general comments for the front mount vertical shake condition

apply here as well. Note that the model accurately predicts the changing sensitivity of the cabin sidewall

and airspace to force inputs in the vertical and axial directions. That is, for the vertical shake condition

measured and predicted response remains fairly constant while for the fore-aft shake condition, both

clearly rise with increasing frequency.

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Using the refined model, the effect of modeling the cargo compartment acoustic space was evaluated. A

finite element mesh of the cargo compartment was generated that interfaced with lower sidewall and

floor structural nodes. The cabin acoustic model interfaced with the same floor nodes (fig. 16) allowing

coupling between the two compartments. Predictions show small differences to the cabin acoustic re-

sponse most notably at the cabin acoustic resonance and at a cargo compartment acoustic resonance,

|

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(b) BS 1010 GE Slde Stringer 12

Radial Frame Response

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(d) BS 1010 GE Side Window Seat Microphone

Figure 18. Finite Element Prediction Versus 727/GE36 Demonstrator Test;Ground Vibration Test- Front Mount Vertical Shake

_-U_01_-23

which occurs at 32 Hz. However, the general characteristics of the response are not changed and further

studies were completed without the cargo compartment model.

A study was also completed to help define minimum modeling size requirements. It was noted that the

tremendous size of the finite element model made model checkout and predictions time consuming and

expensive. A series of model size reductions were previously described (fig. 17). These models were used

to predict response to several shake conditions in order to assess prediction costs and associated accura-

cy. Table 3 gives cost and model size comparisons for each model as referenced to the baseline (refined)

25

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Frequency, Hz

Longitudina/ VariationsAround BS 1010-GE Side Window Seat Microphone PredictionO-UgO 196-24

model. As can be seen, 40% to 60% reductions in computing costs were achieved as well as up to 40%

reductions in model size. Figures 23A and 23B compare the baseline model to the reduced models for

passenger cabin sidewall and acoustic response, respectively, for an aft lower mount vertical shake con-

dition. The results shown in figure 23 are typical for all the shake conditions. It was felt that reduced

models A and B still gave reasonable results, but that complete elimination of the tail, wing, and forward

body structure (reduced model C) degrad e pred!ctions to unacceptable levels within the frequency range

studied. A further comparison that more clearly illustrates this conclusion iscontained in figure 24. The

importance of gross airplane modes in prediction transmission and radiation of engine vibration noise

within this frequency range has been noted previously.

The refined model reflects a valid representation of the 727 demonstrator airplane per production draw-

ings. Inclusion of trim structural and seat absorption models might offer some improvement although

tap tests and noise surveys completed during ground tests indicate the main effects would occur at more

26

I

I

I

II

i

I

i

i

i

i

i

I

i

[]

[]I

I

I

|

|

[ z

L.=u

i

R

!

-5"

i

= _w

M

=

100

90

80

i13_70

8

i°50

40

z

10

1987 FEM GVT data--_

prediction _ \

\ /--1988 FEM _.

I predicti°n ,._

.,.;o,o, js ,_. /" •

t'. ,-.i

i'_.... /" ... ! ,/ "./Y,D: il

"..." il

100

0 I I

10 20 30

Frequency. Hz

(a) Aft Lower Engine Mount Lateral Shake

Figure 20.

40 4O

9O

m 80 1987 FEM

prediction 1988 FEM

70 _.. predic_on-_

6o i.! .... ,• ,',.,.' .'.;,. ._... ,' .... "... ,_-,r:.... ?'.."_:'t '"....'#.... \ ' ', '

40 i;,_._<_.-_" _ i ._ . _ / ", /

,, ,., , - \j

",lz 20 "--- GV'I" data

10

0 _ !

10 20 30

Frequency, Hz

(b) BS 1010 Alile Microphone

Finite Element Prediction Versus 727/GE36 Demonstrator Test,"Ground Vibration Test-AftLower Mount Lateral Shake

_-U_O196-25

than 40 Hz. The extremely complex empennage and strut structure, modified for the GE36 engine, make

modeling difficult and may lead to some problems that would not be encountered in more conventional

structure. Given the above comments and the results presented in this section, it is concluded that finite

element models can be used to predict differences in cabin noise and vibration sensitivity to engine un-

balance forces for different force levels and directions and for different aircraft configurations. Howev-

er, the ability to predict absolute levels at discrete frequencies, with accuracy typically required to make

cabin noise guarantees, has not been demonstrated.

Other studies with the model for flight predictions have shown that the phase relationships between

multiple input forces can shift predicted cabin noise levels 20 dB or more. This result has beenvalidated

independently on flight tests of conventional turbofan aircraft. Thus, the analyst also needs a good un-

derstanding of engine response characteristics in order to assess cabin noise at engine rotor frequencies.

Model reduction studies indicate that within the frequency range studied in this effort, some representa-

tion of the entire aircraft is required. That is, low-frequency whole body and wing modes can contribute

to transmission and radiation of engine rotor noise. This effect diminishes with increasing frequency.

Therefore, the analyst should have some understanding of the aircraft response modes versus the fre-

quency range of his interest in order to determine model size requirements.

27

iJ

I 'it I '| Bulkhead Accelerometers Fore-Aft Response t Floor Accelerometers Vertical Response

_o 1 F &. I"_60 Range of GV'I"data "_ 60

i,_.:.t • _. . !, .. ..,,%. : .'_._.,,,-

I:' ! " F

o 1t'_ I , '_W." I10 20 30 40 10 20 30 40

100

°:LFrequency, Hz Frequency, Hz

BS 1010 Frame Accelerometer Radial Response

7o

50

40

_ 2oz

lO

010

-- Range of Gv'r data

F_eqicfi°ni_

-:...._:,,%,,

I

I I20 30 40

Frequency, Hz

100 1 Cabin Seat Microphones

9O

70 I--- Range of GVT dab

_- . 2"

10 -- FEM predictions

I I _t010 2O 30 40

Frequency. Hz

mm

II

|

i

m

i

i

Figure 21. Finite Element Predictions Versus 727/GE36 Demonstrator Test;Ground Vibration Test-Front Mount Vertical Shake

_UgO186-26

IB

N

m

tl

28M

iiL

L

= =

iii

i

W

=.......

100

9O

8O

70

50

_ 4o

z

20

10

.

0

z

010

IO0

9O

8O

70

60

50

40

3O

2O

10

Bulkhead Accelerometer= Fore-Aft Response

Range of GVT data

_:_ii_ ::'i:_: ,, ,.-..,. :,'._: ....../-V ""

20 30 40

Frequency, Hz

flO"0

z

100

9O

8O

70

6O

50

40

3O

2O

10

010

Floor Accelerometers Vertical Response

,/,, FEM predictions/

.., • .! • ._ =_

_ _. - , ,.',"_ -..-.;

,20 3O 4O

Frequency, Hz

010

BS 1010 Frame Accelerometers Radial Response

FEM predictions _,

p._,. o.

20 30 40

Frequency, HZ

133

z

100

9O

80

70

6O

5O

40

3O

20

t Cabin Seat Microphones

Range of GVT data,

,,.. ,,',_.,_ t- _,_i __

_',_'_k'"" /"- "" "(VL............. /

10 --

I I0

10 20 30

Frequency, Hz

Figure 22. Finite Element Predictions Versus 727/GE36 Demonstrator Test;Ground Vibration Test-Aft Lower Mount Fore-Aft Shake

4O

9-UgO196-27

L

--_._

29

rnnO

N

Z

100

I8O7O

6O

5O

4O

3O

2O

10--

0I0

Full Model

Range of FEM

GVT data predictions

e ;1',_

I I

100

9O

8O

_= 70

i°5(1

I°Z

20

10

|

Jmi

[]I

_ Reduced Model A

FEM

predictions_

Range of

GVT data

t I20 3O

Frequency, Hzo |20 30 40 10 40

Frequency, Hz

Reduced Model B i90 -- Reduced Model C

80 I 80 --== _ Range of Gv'r"data |

r _ .J FEM predictions,_.,..:.,i,_!::.il/_,-.".,.J_ 70 _ . ,-._:_'i,"

:1

I20 20

10 10

0 010 20 30 40 10 20 30

Frequency, Hz Frequency. Hz

(a) BS 1010 Frame Accelerometers Radial Response

Figure 23. Finite E/ement Predictions Versus 727/GE36 Demonstrator Test;Ground Vibration Test-Aft Lower Mount Vertical Shake

4O

g-ug0196.28 f

IB

30

g_

B

mmz

B

w

_qw

m

W

L

HH

E--

6

U

W

100 100

9O

o0•o 80

7O

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))z

CO

nO

iI)

z

Full Model

90

m80

7o

iI

z

Range ofGv'r data

-_:2:.,,_at,

10 FEM predictions

o I I10 20 30 40

Frequency, Hz

100 100

_9_3t Reduced Model B 90co•o 80

| FEM pr_ictions.70_-- _,,_. Range of L_ _ 70

/ _'_'_%'_i_'" GVT data _..,K7" "¢

i,o4O

' ! 130

10 10

o I I o10 20 30 40 10

Frequency, Hz

(b) Cabin Seat Microphones

Figure 23.

m

60

5O

40

3O

2O

_o _-o II0 2O

Reduced Model A

Range of GVT data

"_ predictions

I3O

Frequency, Hz

Reduced Model C

m

• .,j FEM predictions

i.'_ _ _::>.. % _ , .'.._#- "

'+l ".. ,." •,-,¢,.,:::/... I

I l2O 3O

Frequency. Hz

Finite Element Predictions Versus 727/GE36 Demonstrator Test,Ground Vibration Test-Aft Lower Mount Vertical Shake

40

4O

9-Ug01g_28a

r_=,,,,,=,_

L

31

r_

100

9O

=08O

70

_6o

o20

10

010

lOO

9O

=08O

_70

C

_ 4o

N

7° 2o

10

010

Full Model

-- Range of GV'I"data---_L

,^..-. _-_,_.]

I 120 3O 40

Frequency. Hz

Reduced Model B

-- FEM predictions _

!" _!i;'_! :,..'

100

Reduced Model A9O

! ,o_ x_ 6°- .'__t,, -._'--

20 F _ _ " Ra_ngeof GVT datat;

10 --_

' I I01

10 20 30

=0_o

._ 70

_o0e_

-_ 5t?t-

_ 4o

z 20

10

I I o20 30 40 10

Frequency, Hz

Frequency. Hz4[

Reduced Model C

. ,,/,_/_-.-- FEM predictions

,'J ,;..,,\_ //'_J'-_..:, ,.. __ ,.-.

i& "-_ \'..... :..'_'_.,,.._,,/_', ','_ -...,_,_

_ta _'_ n

• I I20 30 ,_

Frequency, Hz

Cabin Seat Microphones

Figure 24. Finite Element Predictions Versus 727/GE36 Demonstrator Test;Ground Vibration Test-Aft Lower Mount Lateral Shake _U_01_8-2_

==

I

m

|

i

i

|

i

i

mm

i

|

II

32

Im

i

II

i

L_

-y-,

w

U

W

=--7

i

t---.

i

L

L

g

Table 3. Modefing Time and Cost Comparison for 727 Demonstrator Airplane Finite Element Models

Model

BaselineReducedmodel AReducedmodel B

Reducedmodel C

Scaled numberofstructuralnodes

1.00 I1.00 I0.67 I0.65 I

I

i

Scaled numberofstructuralelements

1.00

1.000.710.61

Scaledcostofmodalcalculation

0.64

0.440.330.28

i

i Scaledcostof one I Scaled cost ofmodalplusone

I forced response I forcedresponseI caJcula_on 1 calculationI II 0.36 I 1.00I 0.15 I 0.59I 0.29 I 0.62

I 0.16 I 0.44I I

U_1_R1-3

4.4 STATISTICAL ENERGY ANALYSIS RESULTS (FY 1987)

Statistical energy analysis models were developed to predict response for the rotor frequency range and

the propeller frequency range. Predictions were compared to engine strut shake, side-of-body shake, and

flight test conditions.

Unlike the finite element analysis, which used specific structural and acoustic modes, the SEA models

relied on predicted mod.' densities within each substructure to calculate power transfer to the passen-

ger cabin structure and airspace. Specific mode shapes for frequencies were not calculated, rather a

statistical description of modes and interaction of modes with adjacent substructures was used. Thus,

predictions for structures with higher modal densities tend to be better. As part of this effort, it was

found that the dimensions and physical properties of aircraft structures tend to give low modal densities

for the frequency ranges studied.

Low-Frequency Model

Low-frequency (rotor) model predictions were made up to 100 Hz for eight strut shakes, one side-of-

body shake, and one flight test condition. The model was felt to be valid over this frequency range despite

lumped mass representation of the interior trim. Results from the midfrequency (propeller) model

showed energy transfer from the trim to be small compared to that from sidewall structure modes.

Example comparisons of ground test data with low-frequency model predictions for lateral and vertical

strut shake condition are given in figures 25A through 25D and 26A through 26C for the strut, fuselage

sidewall, floor, and acoustic space. The predicted average represents the space average response for the

subsystem. The 95% confidence intervals represent the range or variance predicted for response at indi-

vidual locations on or within the substructure (up to 95% confidence). All of the available measured data

on or within the subsystem were compared to the prediction.

The following general observations were made:

1. For the most part, the data fell within the predicted confidence interval, although the interval ap-

peared to be somewhat greater than the corresponding ranges of measured data for the lateral shake

condition and somewhat less for the vertical condition.

33

813

m

•o 70==

==6o

40

0 0 20

70_

¢0

_6O°

4oZ

30

00 20

I

(a) Strut Vibration Levels ,q Measured] 70 Co)Section 46 Sidewall Vibration /, _ data I I

I i '• • $

40 60 80 100 120 140 160 180 200 O0 20 40 60 80 100 120 140 160 180 200

Frequency, Hz Frequency, Hz

(c) Section 46 Floor Vibration Levels

70

40 60 80 100 120 140 160 180 200Frequency. Hz

Legend:

95% confidenceJ :[ SEAMTM predicted average-intervals I ]: 25-element model

6O0313

¢50

.i

z_

2O :120

(d) Section 46 Interior Noise Levels

h,..:.',• g/<a.2, ',., ,

.\=.,,, .-.

\i: "_-, , ,,.:, v,'.' , , ,

40 60 80 100 i20 i40 160 180 200Frequency, Hz

Figure 25. SEAM TM Predicted Levels Versus 727 Demonstrator Test Data;GVT-Forward Mount Lateral Shake

|miiB

mB

_-Ug01 _30

2. The data peaks were in generally good agreement with the upper limit of the confidence interval, but

the predicted average exceeded the data average at many frequencies. iil

3. The rise and fall of the data mean with frequency was not predicted by the model, particularly for

strut and acoustic response. I

For the lateral strut shake condition, the large confidence interval was due to uncertainty in predicted

power input to the strut inplane subsystem. This uncertainty results from the low modal density of the

strut inplane subsystem• For any structure, the range between maximum and minimum levels will in-

crease as the modal density is decreased.

I

=34

m

I

1

L

=.=

r _

r_w

w

7-i

w

2

=

w

80

". I,', I

8.i

Ii ,,./z

/,f_\ s Measured

,'.-.', \ / data, '_ -,\ ,\t ,

ill v

'k/J.-- .I. "",.,"

,07

0 20 40

95% | T SEAMTM predicted

confidence | T average- 25-elementintervals ( model

Figure 26.

I I I I I60 80 100 120 140

Frequency, Hz

(a) Strut Vibration Levels

70

iiE0Z

ao_-.Z0

I I I160 180 2OO

95% confidenceint rvals

+7

,. ,°

1

80

==:_ r° f

1

z40

0

95% confidence I T SEAMTM predicted

intervals l.L average - 25-element model

& , • , °

o-° i.. l+ _ • /a; • ' ,'"-• ,- ;_,!_,_-"_, "_"",.... .--_" _..._,\.'-"x_,-:,"'-..-:A_,¢i,, ,. I, ,- ;, , ,..,.,..,U.,::"_,,.. " /

20 40 60 80 100 120 140 1613 180 200

Frequency, Hz

(b) Section 46 Sidewall Vibration Level=

t SEAMTM predictedaverage- 25-element model

,,! %'...

Measuredda_

0 20 40 60 80 100 120 140 160 180 200

Frequency, Hz

(c) Section 46 Interior Noise Levels

Low-Frequency SEAM TM Mode/Predicted Leve/s Versus 727 Demonstrator Test Data;GVT-Forward Mount Vertica/ Shake

g-UgOlg6-31

It was found that for this and other test conditions, the response at locations away from the drive point

were overpredicted by a biased amount. This indicted that predicted power inputs, corresponding to the

measured input force, were too high although the transmission modeling is correct• (This may seem at

odds with the underprediction of strut response shown in figure 25A. However, the measured data are at

the end of the strut near the drive point and does not accurately represent average strut response or

power.) The overprediction of power input was related to modeling the drive point structure as an un-

bounded system.

Finally, the failure of the model to predict variations of the mean was attributed to low modal densities in

the actual aircraft structure in this frequency range• This led to the possibility of individual modes domi-

nating response. In this case high strut response near 40 Hz and a cross-cabin acoustic mode near 50 Hz

appeared to combine to give the broad peak in acoustic levels•

35

Bycomparingfigures25and26,it wasnotedthatthemodelpredictedtheverylargemeasureddifferencein strut responsefor the lateralandverticaldriveconditions,aswellasthemuchlowerinteriornoise.Thisagainindicatedthetransmissionmodelingwascorrectandthat SEAis capableof predictingair-craft responsetrendsat lowfrequencies.

MidfrequencyModel

Midfrequencymodelpredictionswere made for two strut shake, three side-of-body shake, and one flight

test condition. Originally, it was planned to make predictions for more GVT conditions. However, the

additional time and budget expended on the initial modeling effort (400-element model) and subsequent

revisions precluded this.

Evaluation of the model concluded that composite-bending stiffness modes of thi_ sidewall dominated

energy transfer to the passenger cabin when compared to trim-panel-bending and skin-membrane-

bending modes. The same observations made for the low-frequency model generally held for compari-

sons of mid-frequency model predictions to test. Predictions tended to be somewhat better and the

influence of individual modes was minimized in this frequency range. The test arena acoustic space was

represented by three space subsystems rather than one (in the low-frequency model) and falloff in level

versus body station was accurately predicted. Figure 27A presents sample midfrequency model predic-

tions for a GVT strut shake condition. Again, the strut response appears underpredicted, but note that

all the measurement points are at the end of the strut. Figure 27B shows predictions for sidewall vibra-

tion levels, and figure 27C shows predictions for aft interior noise levels.

Flight test predictions were hampered again by the inability to estimate input power, a situation also

noted when using PAIN as described later. In this case, measured accelerations were used to develop

input forces. Predicted responseSdownstream of the strut shoWed consistent bias levels (overprediction)

with respect to the measured data. This indicated that estimated power was again overpredicted but that

energy flow was accurately modeled.

Based on the results presented, it was concluded that SEA shows promise in providing relatively simple

models for evaluation of low-frequency noise and vibration transmission. The mean and variance esti-

mates provided by SEAM TM are useful to the designer in that the upper bound of predicted response

can be compared to requirements for maximum allowable noise and vibration. The power flow analysis

feature can be useful in guiding design type and application of suppression hardware.

Two areas of study were recommended including investigation of power input estimation techniques and

improved modal density estimates for low-frequency problems.

In this effort, excitation loading (input power) was developed from input forces and conductance of the

strut (or body) derived from the SEA model. Results showed the response to be consistently

overpredicted, while the rate of response falloff (with distance from the drive point) was accurately pre-

dicted. This suggested that the input power was overpredicted. In the model, the input power was pre-

dicted in terms of the average conductance of the subsystem (associated with the drive point), with the

36

m

l

il

Z

m

m!

I

J

l

[]

[]

I

mm

[]

i

m

u

m

m

I

I

|

[]

|

n

i

D

i

L_

'iW

• _ f//,_,_ .,, "., __ confidence| average- 100-elementmodel70 -- ; f \ ) i _ a/ % _ _' _ /._/-" _ 70 i._nntervals - (prediction normalized at aft fuselage]

-", , ',, ,:,,,,,,,! ,xj I l i'"'.,' .. ,-, t,, r

50- I ', i,_ Measured / ..L 50- ..--. ,.. ; ... ,-.. , ,.,

,,//data 95% l''J average -IO0-eIementSEAMTMpredicted :::!. /: '...........,, /: "'... : .....',k,'I.. . ..,-

Z4_0_7_ _. ¢onnaence [ j model (prediction z40{ j"" i'"" 7intervals normalized at aft fuselage) M u

I I 1 1 I I I I I I0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200

Frequency, Hz Frequency. Hz

(a) Strut Vibration Levels (b) Section 48 Sidewall Vibration Levels

{_ SEAMTMpredicted

80 !T 95% confidence average - l O0-element model

intervals (prediction normalized at aft fuselage)

L,A ii Measured

-_ _ , _." [<_i'..,.

oz I I I 1 I _ I I I I '_10 20 40 60 80 100 120 140 160 180 200

Frequency. Hz

(c) Section 46 Aft Interior Noise Levels

Midfrequency SEAM TM Mode/Predicted Leve/s Versus 727 Demonstrator Test Data;GVT"- Forward Mount Vertical Shake

0-Ug0106-32

Figure 27.

average encompassing at least one resonance frequency of the subsystem. At frequencies below the first

subsystem resonance, the input power will be incorrectly predicted. Some method for handling these

cases must be developed.

It was noted that the SEA predictions do not follow variations with frequency of the measured mean

response. A review of data indicated that low modal density in the aircraft structure may result in re-

sponse that can be dominated by a few individual modes. Because SEA does not calculate specific

modes, it will not tend to predict this behavior. For example, a cross-cabin acoustic mode near 50 Hz

seemed to influence measured noise levels, but the SEA model only predicted modal densities based on

volume of the acoustic space. In this low-frequency range, it was recommended to study how SEA could

be augmented by modal density estimates from simple models of selected subsystems. These models

would represent closed form or finite element solutions that couid predict specific modes.

37

m

i

4.5 REVIEW OF SEA PROCEDURES FOR LOW-FREQUENCY PROBLEMS

Before modifying the SEA models to improve predictions, a number of studies regarding SEA proce-

dures and potential enhancements for low-frequency problems were undertaken. Tasks were defined for

evaluating methods to improve modal density estimates (including the use of finite element modeling), to

improve input power estimates, and to improve variance predictions.

The modal density is an important element in the calculation of statistical energy analysis parameters.

For continuous systems, the number of modes with resonance frequencies in a given band (the mode

count) is determined from the modal density. The mode count relates the modal energy to the mean-

square response. Impedance functions, which, along with prescribed mechanical or acoustical sources,

determine input power to SEA subsystems, are calculated from the modal densities. The modal density

also enters directly into the relationship between coupling loss factor and the coupling parameter use in

the matrix formulations of the SEA power balance equations. Finally, the modal density forms the basis

for a statistical description of the resonance frequencies. In such a description, the resonance frequen-

cies are assumed to be random "events." The modal density specifies the mean rate of occurrence for

these events per unit frequency. Methods to improve modal density estimates are described below.

At high frequencies, the modal density of a continuous dynamic system can be shown to approach an

asymptotic limit that depends on the dimensions of the system. These asymptotic limits are written as--

Ln'-D(w) = -- (la)

_Cg

n2_D(w ) = kA2_Cg (lb)

k2V

n3-D(0_) .= 2_2Cg (lc)

where Cg is the group speed for the system, k is the wavenumber, and the geometric parameters L, A, and

V refer to the length, area, and volume of the system, respectively. The asymptotic forms for the modal

density are valid at high frequencies regardless of the boundary conditions and can be applied to both

structural and acoustic systems as long as the correct wavenumber and group speed are used.

4.5.1 ACOUSTIC SPACE MODAL DENSITY ESTIMATE

The modal density for acoustic spaces can be determined quite simply from the asymptotic forms for the

modal densities because the wavenumber and group speed are related to the radian frequency and the

speed of sound in the acoustic media. The asymptotic forms for the modal densities are useful for acous-

tic spaces that can be idealized as one, two, or three dimensional. Most spaces, however, can be idealized

in this way only over limited ranges of frequency. In general, the modal density of acoustic spaces can be

described as the sum of one-, re'o-, and three-dimensional asymptotic modal densities,

g

ii

i

I

m

m

I

m

l

E

,!

I

mU

!

[]

mm

U

U

m

[]

38 mi

II

lIII

L_

k_

IRi

U

i

w

i

i

i

L oaA oa2V= -- + + -- (2)n(co) 2 =cg

where the parameters are selected to provide the best representation of the modal density for the acous-

tic space over the entire frequency range of interest. This form of the modal density provides three geo-

metric parameters that can be adjusted according to modeling rules for specific types of acoustic spaces.

Generally, the first term is selected to obtain the desired modal density at low frequencies, where one-

dimensional modes dominate. The second term is selected to obtain the desired modal density at midfre-

quencies where two-dimensional modes dominate, and the third term is selected to obtain the desired

modal density at high frequencies where three-dimensional modes dominate. In some cases only two of

the three terms in the general expression will be needed. Example calculations for the 727 demonstrator

airplane are given in section 4.7.2.

4.5.2 STRUCTURE MODAL DENSITY ESTIMATES

The modal density of a structural subsystem can also be obtained from the asymptotic forms for the

modal density given by equations 1. In general, a structural subsystem may have different types of

modes, e.g., bending, inplane compression, inplane shear, and torsional vibration modes. The different

types of modes are usually placed in separate SEA subsystems. As part of this study, general modal

density expressions were developed for each type of mode. To use these expressions requires that a wave-

number and group speed be determined for each type of mode. However, the calculation ofwavenumber

and group speed is more complex than for acoustic spaces. For the 727 demonstrator airplane model,further studies were limited to the use of finite element models or measured data.

4.5.3 USE OF FINITE ELEMENT MODELS TO VERIFY SEA PARAMETERS

Statistical energy analysis is an effective technique for modeling complex dynamic systems having many

modes of vibration. SEA is generally perceived to complement finite element modeling by providing a

prediction procedure at high frequencies where the great number of degrees of freedom required for

finite element modeling is prohibitive. Finite element models can also complement SEA modeling by

providing data to determine parameters such as modal density., power input, and coupling loss factors

for complex structures.

As discussed previously, the modal density is used in the calculation of several SEA parameters. Thus,

an immediate use for finite element modeling is to determine the subsystem modal densities. A finite

element model of an SEA substructure can be used to calculate the substructure resonance frequencies.

The asymptotic values of the modal densities for the substructures of the 727/GE36 demonstrator air-

plane as computed for the low-frequency SEA model are shown in figure 28 over the frequency range 20to 100 Hz. The modal densities of the cabin acoustic space (subsystem 6), the fuselage sidewall (subsys-

tem 5), and the cabin floor (subsystem 21) show an average resonance frequency spacing (inverse modal

density) of approximately 8 Hz. The modal densities for these subsystems are sufficiently large that the

use of the asymptotic form of the modal density should be valid.

39

m

0.5

0.2

0.10.05

0.020.01

0.0050.002

0.001

0.0005

Legend:

0.002

-- I 0.001 __

I 0.0005

i 0.0002

0,00005 I

10 20 30 40 50 60 70 80 90 loo 10 20 30 40 50 60 70 80

Frequency, Hz Frequency, Hz

1 Subsystem 3 (afffusp) 4 Subsystem 16 (pbulkc) 7 Subsystem 16 (pbulkc) * Sb-at bending (sb'ub_)

2 Subsystem 4 (aftfusa) 5 Subsystem 5 (midfusp) 8 Subsystem 21 (miclflc) 0 Strut in plane (strutri)

3 Subsystem 14 (strutrb) 6 Subsystem 6 (midfusa)

Figure 28. Asymptotic Moda/ Densities for the Low-Frequency SEA Mode/

I90 IO0

g-UgO196-33

The predicted modal densities for the pressure bulkhead (subsystem 16), the aft fuselage empennage

structure (subsystem 3), and the empennage acoustic space (subsystem 4) show an average resonance

frequency spacing of approximately 50 Hz. The complexity of the structures and the empennage acoustic

space is sufficiently great that the predicted modal densities should be checked using a finite element

model to obtain a modal density. Because of the fairly large frequency spacing, the use of the asymptotic

forms to predict the modal densities for these subsystems is questionable.

Predicted modal densities for the strut are even smaller. The obvious solution to the SEA modeling

problem for a small modal density is to increase the size of the subsystem. In the case of the strut, a

subsystem could be created that includes the strut, a major section (perhaps all) of the aft fuselage em-

pennage, and the pressure bulkhead. Although the problem could potentially be alleviated in this man-

ner, the procedure of calculating SEA parameters for such a subsystem have yet to be developed.

However, the use of a finite element model would appear to be a reasonable approach to obtaining the

modal density for such subsystem.

As part of this task, a procedure for using finite element data to calculate a modal density was estab-

lished. Briefly, a single substructure is selected to be modeled. Simple boundary conditions are chosen to

approximate bordering subsystems. Eigenvalues are then calculated to a frequency somewhat more than

the upper frequency of interest. At each eigenvalue the frequency spacing to the next eigenvalue is calcu-

lated. The frequency spacings are then inverted to find an "instantaneous modal density," which is

plotted to compare with the asymptotic modal density.

An example of this procedure using the cabin acoustic space is given in section 4.7.2. A new strut modal

density is also calculated in section 4.7.2, but rather than using the FEM predicted frequencies,

4O

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measured modal densities of the composite system were used in a like fashion. Obviously, it is desirable

that the complexity of subsystem finite element models be kept to a minimum otherwise the advantages

of SEA, such as small model size and quick result turnaround, are lost.

A second use for finite element modeling is to determine the input power from prescribed excitations. In

SEA the input power is obtained from a statistical impedance analysis. Finite element models can also

be employed to compute power input and, thereby, provide a means to check the validity of the SEAcalculations.

A third use for finite element modeling is to provide data for calculating the coupling loss factor. Be-

cause coupling loss factors are formulated in terms of modal densities and impedances, improved esti-

mates for the modal densities and impedances will lead to improved coupling loss factor predictions.

4.6 SEAM TM CODE IMPROVEMENTS

In the baseline low-frequency model, the power input to the strut is calculated assuming that the strut

subsystem has infinite boundary conditions. Based on studies completed, the finiteness of the subsystem

and "loading" effects caused by other subsystems connected to the strut should be accounted for.

The input power calculation in the SEAM code has been improved. The input power at a given frequency

or in a band of frequencies is the product of the mean-square force applied to the system and the drive

point conductance (real part of the mobility). When a mass is added to the structure at the point of

excitation, the impedance (inverse of mobility) of the combined system is the sum of the structure imped-

ance plus the mass impedance. In general, the structure impedance is a complex number with real and

imaginary parts, while the mass impedance has only an imaginary part. In earlier versions of SEAM the

mass impedance was improperly set to be real. This resulted in incorrect power input calculations, al-

though the error was not great. The current SEAM code properly calculates the power input using the

correct imaginary value for the mass impedance.

In SEA the predicted variance depends on the inverse of the product of the modal density and the loss

factor. At low frequencies, where the modal densities are small, the variance can be quite large. Again,

considering the effect of bordering subsystems on the subsystem in question, an "effective loss factor"

has been defined that includes both energy dissipation to damping within the subsystem as well as ener-

gy transmitted to connected subsystems.

In order to evaluate the improvements to the SEAM computational procedure, the original and new

input power estimates are shown in figure 29 along with the measured input power for the vertical and

lateral drives, respectively. The SEA mean for the vertical drive condition is 1 to 2 dB more than the

lateral drive condition and in somewhat better agreement with the measured power input. The SEA

mean for the lateral drive conditions is not significantly changed.

The SEAM code provides a prediction for the variance (standard deviation squared) of the power input.

In SEA it is generally assumed that the power input is a log normal distribution, i.e., the variable 10

41

-20

-30

-soi

-60

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;aseqne SEAM VI.861

I, I I I I I I I 1

-20 Improved Version

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Frequency, Hz Frequency. Hz H

(a) Vertical Shake Condition

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;-8.-5o _ _50_ "_

f

fI I 1 I 1 I I I I I -7o [ I I 1 I [ I I I I _-

100 200 0 100 2O0

Frequency, Hz Frequency, Hz

(b) Lateral Shake Condition

SEA mean

SEA mean ± 2 sigma

Measured data

Figure 29. Input Power Comparisons• .UgOlgS-34 j

-60--

-700

Legend:

LOG10 [power input] is normally distributed. Given this assumption, 95% of the power input data in

decibels should fall within a range defined by the mean ,,2 times the standard deviation. Thus, this range

can be used as a 95% confidence interval. In figure 29, the confidence interval has increased approxi-

mately 5 dB to encompass the data for the vertical drive and has decreased up to 5 dB at less than 60 Hz

as desired for the lateral drive, so that the standard deviation is now essentially constant with frequency.

The same trend is true of the response prediction standard deviations.

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4.7 SEA LOW-FREQUENCY MODEL IMPROVEMENTS

A number of improvements to the low-frequency model were made including the input power estima-

tion, new modal density estimates for the cabin acoustic space and the strut, a new estimate for the strut

loss factor, and an improvement to the modeling of the strut connection. Details are given below.

4.7.1 INPUT POWER ESTIMATE

During the ground test measurements, impedances were measured at the drive points. It was therefore

possible to use conductance, the real part of the mobility (inverse impedance), to obtain a measured

value for the power input. The variance in the SEA predictions includes a variance in the input power. By

specifying directly the measured input power in the SEA model, the overall prediction variance can be

reduced thereby improving the prediction accuracy.

The predictions obtained when measured input powers are used directly are given in figure 30 for the

vertical shake condition. The SEA mean is plotted with the mean of the measured data for clarity of

presentation. The predicted results are too high, which indicates that the coupling between the strut and

the empennage is too high. Clearly, simply changing the input power level without correcting the low

strut modal density is not satisfactory.

80

701

_6o__8.

40m

3O

0

\\

I I I I I I I I I20 40 60 80 100 120 140 160 180 200

Frequency. Hz

(a) Section 46 Sidewall Vibration (mldfusp)

Legend:SEAM

_ = Average of measured data

Figure 30.

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x._._/'x\',,j\.

20 I I I I I I I I I0 20 40 60 80 100 120 140 160 180 200

Frequency, Hz

(b) Section 46 Interior Noise Levels (midfusa)

Response Predictions for the Low-Frequency Baseline Model Using Measured InputPower- Vertical Shake

9-Ug0196-35

43

m

il

4.7.2 MODAL DENSITY ESTIMATES

The modal densities for the strut do not include the effect of boundary conditions or connected struc-

tures. A composite modal density, which lumps together both the strut and sections of the empennage,

was determined from the spacing between peaks in the measured input power. These frequency spacings

were inverted to calculate modal density in the same way that spacing between eigenvalues predicted

from a finite element model would be used (fig. 31A). Because modal density cannot be input directly in

the SEAM program, it was necessary to modify the strut properties to simulate the modal density

derived from the measured data. This was accomplished by increasingthe strutlength by a factor of four

while decreasing the strut density by the same factor to maintain a constant strut mass. The comparison

of the SEAM calculated modal density with that calculated from the measured input power peak spac-

ings is shown in figure 3lB.

The use of a finite element model to validate a modal density estimate is illustrated for the cabin acoustic

space. A method for determining the modal densities from finite element models has been discussed. To

demonstrate the procedure, the first 100 modes for the acoustic interior of the Boeing 727/GE36 demon-

strator a_rcraft were computed from a finite element model with 1525 three-dimensional elements. The

resonance frequencies were sorted in ascending order, adjacent frequencies subtracted to compute the

interval between resonance frequencies, and the intervals inverted to obtain an "instantaneous" modal

density. The result of the calculation is shown in figure 32. When presented in this manner the resonance

frequency data appear to be random.

Figure 33 presents the modal density data smoothed over a 10-Hz bandwidth. The data in this plot have

been obtained by counting the number of resonance frequencies in each 10-Hz-wide band and dividing

by bandwidth. The result is a series of data points with a 10-I-Iz spacing, which can now be compared

with predicted modal densities.

In order to more accurately represent the demonstrator airplane test environment, the dimensions of the

interior acoustic space were re-evaluated and modified from those used in the 1987 SEA model predic-

tions. The modal density prediction using the cabin acoustic space volume (52m 3) in equation lc is

shown in figure 33. The estimate is seen to underpredict the modal density obtained from the finite ele-

ment data. The second procedure is to use the general form of the modal density given by equation 2. The

volume was selected to equal the volume of the cabin (52m3), the area to equal the area of the floor

(22.3m2), and the length to equal the length from the lavatory walls to the acoustic barrier (6.1m). The

resulting modal density is also shown in figure 33. The use of the area and length terms improve the

agreement between the finite element data and the prediction. This estimate was used in all further

studies.

4.7.3 STRUT CONNECTION MODELING

It was noted that in the lateral drive model, the strut inplane subsystem is connected to both the empen-

nage and pressure bulkhead bending mode groups. In fact, the strut should only be connected to the

inplane modes of the pressure bulkhead. However, there are no inplane modes of the pressure bulkhead

44

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n( {o2) = n (547.6) = 1/ /k (d 2•=1/341.6 = 2,9E-3

I2O

I I I I I I40 60 80 100 120 140

Frequency, Hz

(a) Modal Density Estimation Calculation Using Measured Data

I I160 180

Legend:Baseline modelStrut 1_2"4, rho/4

* Determined from frequency spacingpeaks in power input data

n(_ I) n(co2)

_.=

I I 1 I I I I I I20 40 60 80 100 120 140 160 180

Frequency, Hz

(b) Strut Modal Density Comparison (strutrb)

Composite Strut Modal Density Based on Spacing Between Peaks in the Measured

Vertical Shake Input Power

20o

2-uo

U90169-36

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I.__ 727 Demonstrator Cabin AcousUc Modes NASA and Boeing FEM Da_

20

0,1

i0.05

p

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I I I I50 100 150 200

Frequency, Hz

instantaneous Moda/ Density for the Cabin Acoustic SpaceFigure 32.

25O

g-Ug0106-37

to excite at the frequencies involved. A better model of the strut connection to the fuselage is a junction

with the strut inplane and the empennage through the mass of the bulkhead, so that the nonresonant

impedance of the bulkhead is taken into account.

4.7.4 STRUT LOSS FACTOR

At this point, predictions were made to determine the effect of the above described changes. It was noted

that predictions were all about 5 dB high including the strut vibration level. Because most of the strut

energy is lost to damping (approximately 80% of the power input to the strut is damped internally), the

high predictions can be lowered by increasing strut damping. This will allow a better comparison of the

power flow prediction capabilities of the model. The damping was increased to a value of 0.24 (12% of

critical), which while arbitrary is not unreasonable considering the strut is a highly bolted structure filled

with hydraulic system components. Results are given in section 4.9.

46

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Legend:StattstJcaJ results using volume term only

0---"-0 Modal density calculated from three-dimensional FEM results

_ Sta_stJcal results using length, area, and volume terms

20 40 60 80 100 120 140 160 180 2(

Frequency, Hz

Figure 33. Comparison of Modal Density Prediction Procedures- Interior Acoustic Spaceg-Ug01 g6-3

4.8 MIDFREQUENCY MODEL IMPROVEMENTS

The midfrequency model was originally developed to predict cabin noise from 100 to 400 Hz for both

strut vibration and empennage acoustic excitation. However, during the effort to improve the low-fre-

quency model, it was found that this model could be used up to 200 Hz for strut vibration conditions.

Thus, efforts to improve the midfrequency model have focused on side-of-body shaker and inflight

acoustic excitation.

The first attempt to improve the accuracy of the midfrequency model was to use the measured power

input. As with the low-frequency model, some improvement was observed although further work on im-

proving modeling accuracy was felt to be needed.

In setting up the midfrequency model, the empennage was modeled using the properties of the skin pan-

els, stringers, and added honeycomb panels. The frames and torsion boxes were not included in deriving

equivalent homogeneous cross-section properties. Above the frequency of the first subpanel resonance,

the modeling assumption is correct. However, at low frequencies the properties must be changed to in-

clude the stiffening effect of the frames and torsion box structure. The complexity of the empennage

structure precludes development of a modeling procedure without use of measured data. The approach,

47

I

NASAN_IOPali A_oP, abt_ _rlcl

Report Documentation Page

1. Report No.

NASA CR-181851

2. Government Accession No.

4. Title and Subtitle

Evaluation of Analysis Techniques for Low FrequencyInterior Noise and Vibration of Commercial Aircraft

7. Author(s)

A. E. Landrnann, H. E "nllema, andS. E. Marshall

9. Performing Organization Name and Address

Boeing Commercial AirplanesP. O. Box 3707Seattle, WA 98124-2207

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationLangley Research Center

Hampton, VA 23665-5225

3. Recipient's Catalog No.

5. Report Date

October 1989

6. Performing Organization Code

8. Performing Organization Report No.

D6-54871

10. Work Unit No.

1I. Conkact or Grant No.

NAS I - 18027

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

t5. Supplementary Notes

Langley Technical Writer: Kevin R ShepherdFinal Report

16, Abs_act

This report documents the application and evaluation of selected analysis techniques for theprediction of low-frequency cabin noise and vibration associated with propeller engine installations.Three analysis techniques were chosen for evaluation including finite element analysis, statisticalenergy analysis (SEA), and a power flow method using elements of SEA (computer program PAIN).Data from ground and flight tests of a 727 airplane modified to accept a GE36 counter-rotatingpropeller engine were used to compare with the predictions. Generally, the comparisons showreasonable agreement, leading to the conclusion that each technique has value for estimatingpotential impact of candidate noise suppression features. However, variations were large enough toremain cautious about prediction of absolute levels for new aircraft. Recommended improvements"

for each procedure are made.

17. Key Words (Suggested by Author(s))

1. Advanced Propeller Engines

2. Analytical Techniques3. Cabin Vibration4. Interior Noise

18. Distribution Statement

Unclassified - Unlimited

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of pages

76

22. Price

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therefore, was to change the properties of the empennage structure so that the predictions of input

power and empennage response would match the data.

Using this procedure the drive point impedance was modified by constructing a model with a frequency

dependent empennage density (fig. 34). Note the very large and abrupt shift that was required to match

data. This seems to validate the above comments regarding modeling accuracy of the empennage, as the

break in density occurs where the first subpanel resonances would be expected to occur. This would

result in a dramatic shift in input power impedance reflected by the large change in density. Compari-

sons with data are presented in section 4.9.

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Frequency, Hz

Figure 34. Midfrequency SEAM Model Variable Panel Density

!400 450

9-U9019_-3,g

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4.9 STATISTICAL ENERGY ANALYSIS RESULTS (FY 1988)

The low-frequency model incorporates the new airspace modal density estimate, the composite strut

modal density, revised strut damping, and the improved strut connection model. Results obtained using

this model are described below.

Response predictions for the vertical shake condition are given in figure 35. Note that predictions have

been extended to 200 Hz. Comparisons with measured data show very good agreement with some

overprediction of acoustic levels at high frequencies. The data falls within the predicted confidence in-

terval, the data peaks are in good agreement with the upper limit of the confidence interval, and in most

cases the predicted average matches the measured average. As was noted earlier, these results were ob-

tained by increasing strut damping to an arbitrary but not unreasonable level. An almost exact match of

the data is obtained when measured input powers are used (fig. 36). Comparisons for fore-aft (figs. 37

and 38) and lateral strut shake conditions are similar to the vertical shake condition.

Because data from the vertical and lateral shake conditions were used in determining parameters for the

improved model, good agreement with data for these conditions is not unexpected. However, the cofn-

parison of the prediction and data for the fore-aft shake condition also shows good agreement, thereby

supporting the general validity of the improvements.

Flight predictions at the rotor frequency fundamental and harmonics were also made. Predictions using

measured GVT transfer functions as the "best" possible prediction were compared with predictions

using SEA estimated transfer functions. In both cases, measured inflight vibration levels were combined

with measured GVT strut impedances to infer forces acting on the strut. Both predictions overestimated

flight levels (by approximately 4 and 6 dB, respectively), but it is noteworthy that the SEA prediction was

within 2 dB of the "best" possible prediction using GVT measured transfer functions.

Comparison of predicted (using the midfrequency model) and measured results for a side-of-body shake

condition are given in figure 39. Because the empennage properties were modified to match measured

response, levels for section 48 (empennage), the bulkhead, and section 46 (passenger cabin sidewall)

match closely. Acoustic levels show good agreement at low frequencies, but are overpredicted at higher

frequencies, a trend seen with the low-frequency model as well. One possible explanation is the absence

of interior trim panels in the models. In 1987 work, it was concluded from preliminary midfrequency

model results that energy transfer through the trim (as compared to composite sidewall modes) was not

important. In light of the most recent findings, this conclusion should be re-examined.

Predictions for flight conditions were again evaluated by comparing results using GVT measured trans-

fer functions and SEA predicted transfer functions. Levels were estimated at fundamental and first har-

monic blade-passage frequencies. Input power was determined by using measured exterior sound

pressure levels and the GVT determined transfer functions. A power input was obtained by multiplying

the measured exterior pressure by an effective excitation area to obtain an equivalent force input. This

area was selected so that the average interior sound pressure level, predicted using the GVT transfer

functions, was equal to the average interior level measured in flight. A prediction was then made using

49

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fI

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Frequency, HzLegend:

SEA mean

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20 40 60 80 100 120 140 160 180 200220

Frequency, HZ

SEA mean + 2 sigma-- -- -- Measured data

Response Predictions for the Low-Frequency Improved Model- Vertical ShakeL_O196R1-40

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g

Section 48 Sidewall

Section 46 Floor I

1 I 18O

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I 1 I I 1 I I I I I20 40 60 80 100 120 140 160 180 200 220

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Figure 36. Response Predictions for the Low.Frequency Improved ModelUsing Measured Input Power Vertical Shake

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Figure 38. Response Predictions for the Low-Frequency Improved Mode/Using Measured InputPower Fore-Aft Shake

g*Ug01 @6-43

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Figure 39. Response Predictions, Midfrequency Model Side-of-Body Shake, Improved Model9-U90196R 1-,44

the same area but with the SEA transfer functions. With this procedure, SEA predictions were reason-

able when compared to measured results at the blade-passage frequency, but high at the first harmonic

(fig. 40). This is comparable to results obtained for GVT comparisons. One interesting result of this

study is the small size (2400 in2) of the empennage area used to convert measured pressure to power

input. This result is very similar to conclusions from PAIN studies (sec. 4.11). That is, cabin propeller

noise seems to be controlled by excitation of a small area by intense sound pressure levels opposite the

fan blades. This result could be important to the designer in locating and optimizing acoustic

treatments.

As with finite element modeling, SEA has not demonstrated an ability to predict absolute levels in the

aircraft. However, as a result of these studies, a number of important conclusions were reached. First,

the method can accurately predict energy flow within the structure as well as trends shown with changing

frequency and excitation directions. Subsystems should be reviewed for modal density levels. Estimates

for those subsystems with very low modal densities might be re-evaluated, perhaps by considering

expanding the subsystem size or by considering the effects of neighboring subsystems. A procedure for

validating modal density estimates using subsystem finite element models was developed.

Particular attention should be paid to the subsystem subjected to excitation forces. That is, the input

power calculation has been shown to be critical and a more detailed understanding (than offered by

SEA) of this subsystem may be required for low-frequency predictions. Again, selected use of finite

element models to define or validate SEA parameters may be appropriate.

4.10 PAIN ANALYSIS RESULTS (FY 1987)

Predictions were made and compared with measured propeller-blade-passage frequency interior noise

for three flight conditions. These included both cruise and holding conditions as shown in table 2. En-

gine power was set accordingly.

PAINUDF allows prediction of explicit empennage and passenger cabin structure modes. Structure re-

sponse modes are based on a floor stiffened cylinder for the passenger cabin fuselage or stiffened plates

for the empennage. In principle, power transfer can be calculated on a mode-by-mode basis. In this

analysis, power transfer from the exterior pressure field to the empennage, from the empennage to the

Blade-passage frequencies and harmonics

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SEA transfer functions

Aft cabin + 3 -6

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passenger cabin fuselage, and from the passenger cabin fuselage to airspace was calculated using the

structural modes. A power flow diagram for PAINUDF is shown in figure 41. The bulkhead junction

between the empennage and fuselage influences the flow of energy between these elements. However, the

bulkhead itself is incapable of transferring power (such as between the empennage and fuselage acoustic

spaces).

For this effort, noise levels measured on the exterior of the empennage of the airplane were used in con-

junction with estimated exterior noise phase behavior based on propeller systems having only one row of

blades. Dummy phase data were required because the density of exterior test microphones was insuffi-

cient to produce accurate measurements. For the first two flight conditions (mach--0.8 and 0.72), the

two rotor speeds were sufficiently separated to extract data for the tone levels associated with the for-

ward rotor only. For the holding condition (mach = 0.42), contributions from the forward and aft rotors

could not be separated. Thus, predictions for each rotor were made using phase estimates for a forward

downsweeping blade row and an aft upsweeping blade row.

Comparison of predicted and measured cabin noise levels is given in figure 42. For the cruise conditions,

agreement between predicted and measured space average values was very good, within 1 dB. At the

holding power condition, a large difference was noted that was attributed to the contribution of the aft

rotor. Time and contract budget constraints did not allow further investigation of this difference. A

fus

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check was made that showed no statistical difference (bias) between the measured and predicted results.

The standard deviation was calculated to be 4.7 dB.

I

iFlight condition

Mach = 0.80 at 35 000 ft

Mach = 0.72 at 35 000 ft

Mach =0.42 at 10 000 ft

Rotor

Forward

Forward

Forwardand aft

BPF frequency, Hz

169

170

180

Predicted minus measured levels, dB

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iFigure 42. Measured Versus PAINUDF Predicted Levels

Q-UgO196R!-47

It was concluded that PAINUDF showed promise in providing models to predict propellei'-blade-

passage frequency interior noise for large commercial transports. Based on the FY 1987 results, a num-

ber of recommendations were made regarding further analytical studies and exploration of potential

PAINUDF improvements. Description of these recommendations follows.

It was recommended that predictions for aft rotor noise levels for the holding condition be reviewed to

determine why predicted levels for the aft rotor were so much higher than for the forward rotor.

Experience gained in using PAINUDF showed that flight measured exterior levels were on a much spars-

er grid than used by the program and not of sufficient quality to obtain phase relationships for program

input. A fair amount of work involving interpolation of amplitude measurements and generation of

dummy phase data from a simple propeller blade row engine model were required to generate program

inputs. A study using the current 727 demonstrator airplane model was recommended to evaluate sensi-

tivity to propeller signature amplitude and phase. This would help define input data requirements for

future applications.

It was noted that the empennage representation in PAIN-tSDF was for the rather unique 727 configura-

tion. It was therefore recommended that a more general conical empennage section model be developed.

While predicted and measured space-averaged acoustic levels were within 1 dB, inspection of the datashowed more than a 10-dB falloff from the back to the front of the compartment (fig. 43). The figure

compares the individual measurement points and their relative location to the predicted and measured

space average. Some estimate of peak levels and distribution would be useful to the designer for

placement of acoustic treatments. Thus, a procedure for estimating noise gradients within an acoustic

airspace was recommended.

4,11 PAIN ANALYSIS RESULTS (FY 1988)

Initial activity focused on understanding the anomalous prediction for the aft rotor contribution to the

interior noise of the demonstrator airplane. It was felt that an evaluation of program coding was

57

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Average of Seat Measurements Versus PAINUDF Space Average PredictionFigure 43.

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warranted. As a result of this evaluation, two coding errors were discovered in the PAINUDF program

and were corrected. The results of the code correction changed levels slightly, but did not significantly

affect the large difference between forward and aft rotors.

From this point, the excitation field characteristics for forward (downsweeping) and aft (upsweeping)

rotors were studied. The geometry for the open, curved panel model of the empennage and the relative

position of the UDF engine is shown from the axial view in figure 44. Note that the line of normal inci-

dence is nearer the center of the panel for blade upsweep than the downsweep. This means that in both

cases, some energy from the excitation field cannot be represented, but for blade upsweep a greater

portion of the excitation field is accounted for. Thus, it is reasonable to expect that the blade upsweep

case would give the higher prediction for this particular geometry.

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Propeller Wavefronts for Blade Downsweep (Forward Rotor) and Blade Upsweep (Aft Rotor)at 0 = 105 °

9-U901 _R_-4_

To test this expectation, the axis of the propulsor was rotated downward so that the wavefronts for blade

upsweep and downsweep strike the panel in an identical (mirror image) fashion (fig. 45). Predictions for

this configuration show equal levels for blade upsweep and downsweep. However, predicted levels for

this case were still 5 dB more than those measured on the airplane.

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Figure 45. Propeller Wavefronts for Blade Downsweep (Forward RotoO and Blade Upsweep (Aft Rotor)at 0=80 °

_._01_RF-._

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Although predicted levels remain high, it was concluded that the model is working correctly. The original

aft rotor prediction, thought to be anomalous, has been shown to be consistent with the forward rotor

predictions and is associated with the position of the rotor with respect to the open panel boundaries of

the empennage representation.

Based on the above results, it was decided that the empennage representation should be improved be-

fore further analysis. On the 727 demonstrator airplane, energy from the propeller blade rows is trans-

mitted through the empennage sidewalls as well as the tail surface and bottom of the empennage, which

are not represented by the open shell structure. A conical empennage section was modeled using local

mass and stiffness properties similar to those of the curved open panels. Note that with the full conical

section the entire excitation field can now be represented regardless of engine and strut angle or upsweep

versus downsweep. Cabin interior noise levels were again estimated using the correct propulsor location.

Results are shown in figure 46 and are compared to baseline results using the corrected code. Note that

the differences between the aft and forward rotor are much smaller (but not zero because of the tapering

geometry of the empennage versus blade row position). Also, the aft rotor prediction is now independent

of the direc:ion of rotation. Note also that the expected increase in level, due to the conical structure

allowing full representation of the excitation field, is more than offset by the increased stiffness of the

conical structure. That is, the stiffer (conical versus open panel) geometry results in a lower modal densi-

ty and less efficient coupling with the exterior pressure field.

Because measured phase values are often difficult to obtain or estimate, it was desirable to determine

the level of accuracy necessary for phase description. For a preliminary assessment, predictions using

the model with the open panel empennage representation were made for constant phase, dummy phase,

and rapidly varying phase. Predictions varied dramatically as seen in figure 47. The case of constant

phase yields the highest interior levels and the case for rapidly varying phase yields the lowest

Predicted minus measured levels, dB

E

Flight condition

Mach = 0.80 at 35 000 ft

Mach = 0.72at 35000 ft

Mach = 0.42 at 10 OO0 ft

Mach = 0.42 at 10 0(30 ft

Mach = 0.42 at 10 000 ft

Rotor

Forward

Forward

Forward

Aft

Aft

Rotation

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Downsweep

Upsweep

Down,weep

Open empennage

1.1

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Figure 46. Measured and PAINUDF Predicted Levels for Open Pane/and Conical Empennage Models9-UgOlg6R!-51

w

Flight condition

Math = 0.80 at 35 0(30 ft

Mach = 0.72 at 35 000 ft

Mach = 0.42 at 10 000 ft

Mach = 0.42 at 10 (300 ff

Rotor

Forward

Forward

ForwardAft

Rotation

iDownsweep

Downsweep

Downsweep

Upsweep

Predicted minus measured levels, dB

Dummy phase

1.1

0.1

2.1

8.0

Constant phase

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Rapidly varying phase

-13.1

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Figure 47. Measured and PAINUDF Predicted Levels Phase Sensitivity Study9-UgO'r 96RL52

predictions. Although constant phase over the entire grid is unrealistic, it appears that significant energy

flow from the propeller field to the empennage can be expected from regions where phase varies slowly

and pressure levels are high.

It should be noted that the very stiff empennage structure representation results in low modal densities

(long structural wavelengths) in the frequency range of interest. As a result, this particular model is very B

sensitive to phase variations. Further sensitivity studies to phase variation and receiving structure stir-2

fness are presented in following sections.i

It was felt that to improve 727 demonstrator airplane predictions an accurate estimation of the excitation m

field phase characteristics would be required. To this end, NASA supplied such data using Aircraft MNoise Prediction Program (ANOPP) predictions for the test propeller engine configuration. The =

ANOPP predictions showed more rapidly varying phase than the dummy data, particularly forward of

the propeller plane (fig. 48). A series of predictions were made using the 727 demonstrator airplane mod-

el with conical empennage, measured propeller excitation amplitudes, and either dummy or ANOPP

phase data (fig. 49).

As expected, the prediction using the more rapidly varying ANOPP data is much lower than the predic- R

tion using dummy phase data (case 1 versus case 2). To study phase effects further, predictions using only

Forward rotor prediction 0,8 math,

BPF = 16g Hz

Dummy phase data i___

....... ANOPP phase data Forward A.ftprop I. prop plane plane

(90 line Increments) .,. ,. ..................

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iFigure 48. Comparison of Propeller Field Phase Contours ANOPP Phase Versus Dummy Phase

10-UgDlg6R1-53

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Grid size

Full

Full

Rear-haft

Rear-half

Full

Full

Receiving structure

Empennage

Empennage

Empennage

Empennage

Fuselage

Fuselage

Predicted minus

measured levels, dB

-4.6

-22.9

-11.1

-23.6

13.1

10.2

Figure 49. Measured and PAINUDF Predicted Levels PAINUDF Sensitivity Study to ExcitationModels (Mach = O.80 at 35 000 ft)

10-UgO196R 1-54

the rear-half of the excitation grid were made. For the ANOPP phase data where phase changes rapidly

in front of the propeller plane, nearly all the energy enters through the rear-half of the grid (case 4). For

the dummy phase data the effect is not nearly so dominant (case 3).

Finally, the effect of modal density was studied. As noted earlier, very stiff structures, such as the empen-

nage, will have low modal densities (long structural wavelengths), which will couple most efficiently with

excitation fields of slowly varying phase. Predictions were made by subjecting the fuselage section direct-

ly to the excitation field. The fuselage is much less stiff than the empennage. Cases 5 and 6 of figure 49

now show much less sensitivity to phase than before. Levels are significantly higher because losses

through the empennage structure are no longer accounted for.

Without additional test data to validate excitation field predictions it was felt that further attempts to

improve the PAINUDF 727 demonstrator airplane model would not be useful. The above studies show

that interior noise levels on propeller aircraft can be extremely sensitive to the excitation field phase and

the receiving structure stiffness (or modal density). The analyst must be cognizant of the modal charac-

teristics of the aircraft structure in the frequency range of interest and take pains to describe the excita-

tion field in corresponding detail.

4.12 PAIN IMPROVEMENTS AND FEASIBILITY STUDIES

The second part of the 1988 effort focused on expanding capabilities of the PAIN program. As a first

step, a five layer passenger cabin trim was incorporated. The original two layer model allowed an airgap

oi" layer of insulation and a limp mass trim. The five layer model allows combinations of insulation, air-

gaps, and septa (with damping). An example of a five layer trim is given in figure 50.

A users manual was written and delivered to NASA that describes the aft propulsor version (PAINUDF)

as well as the five layer cabin trim option.

62

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Airgap 1 = element 1 = type 2Insulation = element 2 = type 1Septum = element 3 = type 3Airgap 2 = element 4 = type 2Trim panel = element 5 = type 3

S-Layer Trim (Example)

Examp/e of S/dewa// Layer Conf/gurat/onslO-U_OI_6R 1-55

A number of potential features were studied that could further enhance the capability of the PAIN mod-

el. These features were bulkhead transmission and radiation, exterior pressure loading fore and aft of

the pressure bulkhead, cabin noise caused by engine unbalance, and cabin noise gradient.

To add radiation by the bulkhead, the bulkhead must be included as a fourth element of the system. A

fifth element, the acoustic cavity within the empennage must also be accounted for if transmission

through the bulkhead is to be included. It was shown to be feasible to include the bulkhead as an inde-

pendent element. It is also considered possible to include the bulkhead as part of the integral fuselage-

bulkhead-empennage composite structure as was done in the original PAIN formulation for the fuselage

and floor. Based on the expectation that low-frequency global modes will be important at propeller tone

frequencies, the latter method was recommended.

Two methods for accounting for pressure loading fore and aft of the bulkhead were outlined. In the first

method, it was pointed out that PAINUDF can currently run twice with separate pressure fields on the

fuselage and empennage elements. The resulting interior space average sound pressure levels (SPL) can

then be summed. In the second method, a power balance could be formulated on the three elements of

the PAINUDF system (the empennage, fuselage, and cabin volume). Because it has been shown that the

majority of power inflow occurs over small sidewall sections local to the propeller plane, no further work

in this area was recommended. PAINUDF should be run twice for those cases when significant power

inflow is expected through both the empennage and fuselage surfaces.

PAINUDF can be modified to predict cabin levels caused by engine unbalance in principle by simply

including the strut as an element just as the bulkhead would be included in the first study. However, the

difficulty in calculating the resulting modes of integral composite structure and the low modal density at

63

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engine once-per-revolution frequencies make this enhancement of questionable value and therefore, it

was not recommended.

The interior sound levels measured during flight varied significantly along the axis of the demonstrator

airplane fuselage (fig. 43). Therefore, the feasibility was considered of accounting for the sound level

gradient within the PAIN program. In order to account for the gradient, the power balance formulation

presently used would be replaced by a general solution in which a cavity Green's function is defined with

axial dependency. Space averages will then only be taken over the cross section.

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5.0 CONCLUSIONS AND RECOMMENDATIONS

At the end of the first year's effort, it was concluded that each analysis procedure showed promise for use

in predicting low-frequency noise associated with advanced propeller engine installations. It was noted,

however, that variations between predicted and measured levels were large enough to remain cautious.

The goal of the second year's effort was to explore modeling and analysis techniques to improve results.

Assessment of the second year's results indicate that predictions of absolute levels, with accuracy typi-

cally required to make cabin noise guarantees, have not been demonstrated. However, the models have

demonstrated the ability to predict trends and should be useful to a designer in assessing type and place-

ment of suppression treatments. Thus, it is recommended to proceed by using the models to identify

engine vibration and propeller noise transmission mechanisms and assess potential suppression con-

cepts. Other conclusions are summarized in the following sections.

5.1 FINITE ELEMENT ANALYSIS

One of the initial objectives of the finite element modeling task was to demonstrate that loads analysis

models could be modified for noise analysis at engine rotor frequencies. If possible, this would save a

large amount of modeling effort. The 727 demonstrator airplane model was developed from such a loads

model by adding mass elements for the structure and trim and a finite element representation of the

cabin airspace. The general agreement with measured GVT levels and the ability to predict response

sensitivity to different excitation directions indicate this objective has been met.

The 727 demonstrator airplane finite element model was found to be time consuming in terms of model

checkout and turnaround of predicted results due to its large size. Studies were completed in which the

model size was reduced by simplifying and then eliminating representation of wing, tail, and empennage

structure. Results indicate that whole body and wing modes can contribute to transmission and radi-

ation of engine rotor noise. Thus, some representation of all of the aircraft structure is required. Beamelements for structure not in the direct transmission path were found to be satisfactory. Inclusion of the

baggage compartment airspace did not significantly affect results.

Studies with the model for flight predictions show that the phase relationship between multiple input

forces can shift predicted levels by 20 dB or more. This result has been demonstrated independently on

flight tests of conventional turbofan aircraft and suggests that engine response modes can couple effec-

tively with strut modes to transmit vibration at engine rotor frequencies.

These results indicate that the analyst should have some understanding of potential engine and aircraft

modes in order to properly model the structure and assess cabin noise. It is noteworthy that SEA results,

described below, support these conclusions.

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Studies have shown that the complex structure and low modal densities of the strut and empennage

precluded accurate SEA predictions of input power and therefore, cabin noise levels. When measured

input power from GVT tests was used, the models were shown to accurately predict power flow through

the aircraft to the cabin. Procedures for estimating modal densities and input power using finite element

analysis were developed and demonstrated. It now appears that development of selected small finite

element models to determine input power coupled with SEA models to predict transfer functions to the

passenger cabin forms a viable prediction procedure. In this way, a relatively small model can be devel-

oped that allows noise control engineers to evaluate and influence structural design before configura-

tions are frozen. Final configuration details would be evaluated using finite element models.

Propeller tone vibration and noise levels in flight were overpredicted throughout the aircraft. This led to

the conclusion that input power was being overestimated. This was confirmed by reducing the empen-

nage excitation area used to convert measured pressure to force inputs so that measured empennage

response was matched, resulting in good agreement at all other locations. Another conclusion from this

exercise is that a significant portion of the propeller tone energy appears to enter through a relatively

small portion of the empennage. Studies using PAIN confirm this conclusion and are described below.

Finally, it was noted during these studies that the low-frequency model provided relatively good predic-

tions up to 200 Hz. This implies the more detailed subsystem representation in the midfrequency model

may not be required for predictions at propeller-blade-passage frequencies. Further work in this area is

recommended.

5.3 PAIN ANALYSIS

At the end of the first year's work, an apparent anomalous result regarding prediction of tone level_ from

the aft rotor was noted. These results were explored and found to be consistent with forward rotor pre-

dictions. This is a result of excitation field phase differences for forward (downsweep) and aft (upsweep)

blade rows mapped over the open panel representation of the empennage. The open panel empennage

was thus replaced by a conical representation.

Further studies with this model indicated that cabin levels were very sensitive to the excitation field

phase and that by varying phase, the measured flight tone levels could be bracketed. Because test mea-

surements were insufficient to describe excitation field phase (dummy values were used for all cases),

further efforts to match predicted and measured levels were discontinued. As a result of these studies

however, an important conclusion was reached. As with SEA results, it appears that most propeller tone

energy enters the aircraft through a relatively small area of the empennage where the excitation field

phase varies slowly. This is important because it implies that noise suppression treatments, which are

inherently heavy and expensive, can be concentrated over small areas where power flow is the greatest.

The empennage is a stiff structure with low modal density (long structural wavelengths). When the softer

fuselage structure was evaluated (by exposing it directly to the propeller noise field), it was found to be

66

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less sensi',:ve to phase of the excitation field. That is, the higher modal density of the fuselage allowed

efficient excitation of several modes regardless of the propeller field phase. As with finite element analy-

sis and SEA, this indicates that for low-frequency evaluation of aircraft structures, some knowledge of

modal behavior is required.

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