Measurement of Bulk Materialsweb.engr.uky.edu/~dwherr01/Bandung/11_Bulk_Properties.pdf ·...

D. W. Herrin, Ph.D., P.E. University of Kentucky

Department of Mechanical Engineering

Measurement of Bulk Materials

Measurement of Bulk Properties

Noise and Vibration Short Course

Dept. of Mech. Engineering University of Kentucky

2

Motivation

  Determining the bulk properties ü  Complex wave number and characteristic impedance ü  Complex speed of sound and density

  Bulk properties are used ü  For designing layered absorbers ü  In FEM and BEM models




3

Overview of Approaches

Direct Measurement

Measure Sound Absorption

Measure Flow Resistance

Ø  Two load method ASTM E 1050 Ø  Two cavity method Utsuno, 1989 Ø  Three microphone method Iwase et al., 1998

Curve fit to find flow resistivity based on empirical equations Simon et al., 2006

Curve fit to find Biot parameters based on theory

Find bulk properties from fitted Biot parameters Allard, J. F., 1999

Find bulk properties from measured flow resistivity Wu, 1988; Mechel et al., 2002





4


Direct Measurement


Ø  Two load method ASTM E 1050 Ø  Two cavity method Utsuno, 1989 Ø  Three microphone method Iwase et al., 1998





5 5

Two-load Method

( )

1

,2,1

sin2

111

kseHeH

jAsljk

refjkl

ref+−− −

=

( )

1

,1.2

sin2

111

kseHeH

jBjkl

refsljk

ref −=

+

( )

2

,4,3

sin2

222

kseHeH

jCjkl

refsljk

ref −=

+

( )

2

,3,4

sin2

222

kseHeH

jDsljk

refjkl

ref+−− −

=

For each load:

ASTM E2611-09

1 2

s1 s2 l1 l2

d

A

B

C

D

3 4 x=0

Load a Load b




6

( ) cBAuBAp

ρ/0

0

−=

+=( ) cDeCeu

DeCepjkdjkd

d

jkdjkdd

ρ/−=

+=−

−

Pressures and particle velocities at two ends of the sample:

Four-pole matrix

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−

−

−

−

−

−

−

=

dadbdbda

adbbda

dadbdbda

dabdba

dadbdbda

dbadab

dadbdbda

dabdba

upupupup

upupuuuu

upuppppp

upupupup

T0000

0000

ASTM E2611-09

Transmission Loss Measurement

⎟⎟⎠

⎞⎜⎜⎝

⎛+++= 2221

121110 2

1log20 TcTcTTTL ρρ




7

Load a and Load b

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000Frequency (Hz)

Abso

rptio

n C

oeffi

cien

t

Load A Load B

Load A: Open tube. Load B: Close the tube with 4” absorbing material.

Load B

Load A

ASTM E2611-09




8

Two Load Method

Load 1

Load 2

Loudspeaker

Piston

Impedance tube

Microphones

Sample

1 2 3 4

1 2 3 4

Open

( ) ( )( ) ( ) ⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

dk/zdkjdkjzdk

DCBA

ccc

ccc

cossinsincos

djAzBk

B/Cz

cc

c

⎟⎟⎠

⎞⎜⎜⎝

⎛=

=

arctan

ASTM E2611-09




9

Two Cavity Method

L d

L’ d

Cavity 1

Cavity 2

Loudspeaker Piston

Impedance tube

Microphones

( ) ( )( ) ( )''

''''

c zzzzzzzzzzzzz

1122

11222211

−−−

−−−±=

( )( )( )( )⎟

⎟⎠

⎞⎜⎜⎝

⎛

+−

−+⎟⎟⎠

⎞⎜⎜⎝

⎛=

cc

ccc zzzz

zzzzjd1k

21

21ln2

Utsuno,1989

z2 z1

z2 ’ z1

’




10

Rigid End

L s

Microphones

Loudspeaker

Sample

d x

x = 0

1 2

3 A

B

Iwase et al., 1998

Three Microphone Method




11

jkLjks

jks

eeHHe R 2

12

12−−

−=

Rigid end

L s

Microphones Sample

d x

x = 0

1 2

3

Speaker

Iwase et al., 1998


Reflection coefficient:




12

The complex wave number of the sample is:

231 1cos1 H

ReeR

dk jkLjkLc −

−

+

+=

The characteristic impedance of the sample is:

zc = jz01+ R1− R

tan kcd( )

Iwase et al., 1998





13

1 inch Melamine Foam

Melamine Characteristic Impedance

-4

-2

0

2

4

6

0 1000 2000 3000 4000 5000

Cha

ract

eris

tic Im

peda

mce

Frequency (Hz)

Three Microphone (Re) Three Microphone (Im) Two Cavity (Re) Two Cavity (Im) Two Load (Re) Two Load (Im)




14

Melamine Complex Wave Number


-40

0

40

80

120

0 1000 2000 3000 4000 5000

Com

plex

Wav

e N

umbe

r (1/

m)

Frequency (Hz)

Three Microphone (Re) Three Microphone (Im) Two Cavity (Re) Two Cavity (Im) Two Load (Re) Two Load (Im)




15

Melamine Sound Absorption Coefficient


0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000

Abs

orpt

ion

Coe

ffici

ent

Frequency (Hz)

Two Load

Two Cavity

Three Microphone




16


0

2

4

6

8

10

0 1000 2000 3000 4000 5000

Tran

smis

sion

Los

s (d

B)

Frequency (Hz)

Two Load

Two Cavity

Three Microphone

Melamine Transmission Loss




17

1 inch Glass Fiber

Fiber Characteristic Impedance

-4

-2

0

2

4

0 1000 2000 3000 4000 5000

Cha

ract

eris

tic Im

peda

nce

Frequency (Hz)

Two Load (Re) Two Load (Im) Two Cavity (Re) Two Cavity (Im) Three Microphone (Re) Three Microphone (Im)




18

1 inch Glass Fiber

Fiber Complex Wave Number

-40

0

40

80

120

0 1000 2000 3000 4000 5000

Com

plex

Wav

e N

umbe

r (1/

m)

Frequency (Hz)

Two Load (Re) Two Load (Im) Two Cavity (Re) Two Cavity (Im) Three Microphone (Re) Three Microphone (Im)




19

Fiber Sound Absorption Coefficient

1 inch Glass Fiber

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000

Abs

orpt

ion

Coe

ffici

ent

Frequency (Hz)

Two Cavity

Two Load

Three Microphone




20

Fiber Transmission Loss

1 inch Glass Fiber

0

2

4

6

8

10

0 1000 2000 3000 4000 5000

Tran

smis

sion

Los

s (d

B)

Frequency (Hz)

Two Cavity

Two Load

Three Microphone




21

Comparison

Two Load Two Cavity Three Microphone

No. of Loads 2 2 1

No. of Calibrations 3 1 2

Smoothness of Curve Good Good Excellent




22


Direct Measurement


Ø  Two load method ASTM E 1050 Ø  Two cavity method Utsuno, 1989 Ø  Three microphone method Iwase et.al., 1998





23


Plug into Empirical Models Wu (1988) or Mechel et al. (2002)

Measure Flow Resistivity Using

ASTM C522

Vacuum source

u

ΔP Sample (thickness t )

Flow resistance:

uΔPrs =

Flow resistivity:

trσ s=

Wu, 1988; Mechel et al., 2002




24

Summary

  Compared the various methods for determining the bulk properties of sound absorbers.

  Curve fitting approaches are adequate for common sound absorbing materials.

Measurement of Bulk Materialsweb.engr.uky.edu/~dwherr01/Bandung/11_Bulk_Properties.pdf ·...

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