Sound Absorption Characteristics of Membrane Based Sound Absorbers

7/31/2019 Sound Absorption Characteristics of Membrane Based Sound Absorbers

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Purdue University

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Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering

8-28-2003

Sound Absorption Characteristics of Membrane-Based Sound AbsorbersJ Stuart BoltonPurdue University, [email protected]

Jinho Song

Bolton, J Stuart and Song, Jinho, "Sound Absorption Characteristics of Membrane-Based Sound Absorbers" (2003).Publications of thek b
http://docs.lib.purdue.edu/http://docs.lib.purdue.edu/herrickhttp://docs.lib.purdue.edu/mehttp://docs.lib.purdue.edu/mehttp://docs.lib.purdue.edu/herrickhttp://docs.lib.purdue.edu/


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Seogwipo, Jeju, Korea- ,

Sound Absorption Characteristics ofMembrane-Based Sound Absorbers

,

Jinho Song and J. Stuart Bolton

ay . err c a ora or esPurdue University


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Motivation Recently, it has been observed that

Macro-cellular polyolefin foams (e.g.,Quash-like) absorbsoun energy even oug e oams are mos y c ose -

celled and the average cell size is very large.

*

How does this sound absorption arise? How do you model this effect?

C. Parket al., New Sound-Absorbing Foams from Polyolefin Resins,Proc. of Inter-*

Purdue University Herrick Laboratories

Noise 2000, pp 583-586, 2000


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Quash Membrane Model- To this point, model is based on tensioned membranes

-

Top View of Quash

Membrane



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Foam Modelin Procedure2-D Model Sound Energy Loss Mechanisms3-D Model

Energy dissipation

by membrane flexure

scous ossthrough perforation

Unit cell

Membrane

Material Properties

Tension

Loss factor

Thermo-viscousboundary layer effect

Membrane Density

Surface Film Density

PorosityRigid Frame


Flow Resistance


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Theoretical Model - Permeable Membrane

TRANSMITTED WAVE

INCIDENT WAVE

REFLECTED WAVE

I IIFLUID

TENSIONED, PERMEABLE MEMBRANE

zjk

r

n

n

jkz nz

nerkJBezrP )(),( oI Sound Pressures in

Acoustic Cavities:z

r

n

nnz

nerkJCzrP

)(),( oII

rkJAtr Membrane Displacement

nn

on

o

n

on FrkJFtru n )(),( 0

Membrane Displacement

(Fluid Component):



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Theoretical Model Solution Method

Apply four boundary conditions on a- -

Solution Method

- The Continuities of Velocity at the Both

Boundary Conditions

membrane

Side of a Membrane:

t

u

t

y

z

P

j z

)1(1

0

I

oParticle Position

- The Force Equilibrium Equation in the

t

u

t

y

z

P

j z

)1(0

II

o

I IIr

~

NA

A

...

1

)()1()(

III2

22 PP

Tt

uy

T

R

t

y

Ty

fs

)(2PP

uyR

uh

y

Numberof Point

at which

B.C.s

applied

N

N

C

C

B

B

...

...

0

0

Matrix

tCoefficien

Vector

Forcing

where

o

tt

ffbackfront vRPP AaN /2

)1(o jTT



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Energy dissipation by Membrane

TRANSMITTED WAVEINCIDENT WAVE

Measurement

REFLECTED WAVE

MEMBRANE

Sound Pressurefrom

microphones

Normal IncidentReflection coeff.:R

of Membrane :

Zm = (1+R) / (1-R) -ocEstimation

our er essecoeff. ofIncident / Transmitted

Waves



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Transfer Matrix Method Membrane & Air Cavity Transfer Matrix

mT1

10

mZ

=

s n 12co

))(sin( 12 llkc

i

o

cos 12

))(cos( 12 llk aT =

smT aT totalT mT aT mT aT=

N layers

Top

P

T= BottomP

1 layer

ooTop

Top

cZR

Top Bottom

Reflection Coefficient

1 layer

ooTop

2

1 TopR Absorption Coefficient

N layers



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Ex erimental Set-u

PowerAmplifier

u y

Signal Analyzer

Micro hone

ComputerPre-Amplifier

Source

QuashStanding

amp eWave Tube



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Experimental Set-up

Loadin uash Sam le Measurement Set-u



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Comparison of Measurement and Prediction

m=0.0885 kg/m2, To=0.13 N/m, =1.6, ms=0.1586 kg/m

2, =0.0085,

= = = = =


. , . , o . , . , .


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Parameter Effects on Sound AbsorptionMembrane SizeFoam Thickness

m=0.07 kg/m2, To=0.5 N/m, =0.7, ms=0.2 kg/m

2, m=0.07 kg/m2, To=0.5 N/m, =0.7, ms=0.2 kg/m

2,

= = = =


. , f . , . , o . , . , . , . ,


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Parameter Effects on Sound AbsorptionMembrane PorositySurface Mass

m=0.07 kg/m2, To=0.5 N/m, =0.7, =0.01, m=0.07 kg/m

2, To=0.5 N/m, =0.7, ms=0.07 kg/m2,

= = = =


f . , . , o . , . , . , o . ,


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Parameter Effects on Sound Absorption

ms=0.2135 kg/m2, =0.0,Rf=0.2 Rayls, t=0.0002 m, do=0.0056 m, h=0.056 m,N=12


-


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Some High Absorption Designs

New Design 1

m= . g m ,

To=0.065 N/m (), =1.6,ms=0.1941 kg/m

2(), =0.02(),

Rf=0.286 Rayls, t=0.0002 m,

o= . m , = . m,

N=10()

New Design 2

m=0.1770 kg/m2(),

To=0.13 N/m, =1.6,

ms=0.0970 kg/m2 (), =0.03(),

Rf=0.286 Rayls, t=0.0002 m,

do=0.00583 m(), h=0.0583 m,N=10 ()



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Conclusions & Future WorkAn acoustical model for membrane-based sound absorbing materialswas presented and was verified experimentally on the basis of

.

It has been found that the theoretical model can accurately reproducethe acoustical behavior of the particular foam studied here.

It was shown that the choice of particular combinations of materialproperties can result in improved sound absorption.

The present work can provide the foundation necessary to designmembrane-based sound absorbing materials having enhanced sound

absorption capacity.

The present work implies that alternative stiffness mechanisms of

membrane systems such as flexural stiffness, membrane curvature,bulk elasticity, and membrane inhomogeneity, can also result in sounddissipation in membrane-based foams; this work will be presented in the


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Sound Absorption Characteristics of Membrane Based Sound Absorbers

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