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Purdue University
Purdue e-Pubs
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/7/31/2019 Sound Absorption Characteristics of Membrane Based Sound Absorbers
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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
Purdue University Herrick Laboratories
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,
= = = = =
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. , . , 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,
= = = =
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. , 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,
= = = =
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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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-
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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
Purdue University Herrick Laboratories
.