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Purdue UniversityPurdue e-Pubs
Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering
8-2005
Porous Materials for Sound Absorption andTransmission ControlJ Stuart BoltonPurdue University, [email protected]
Follow this and additional works at: http://docs.lib.purdue.edu/herrick
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] foradditional information.
Bolton, J Stuart, "Porous Materials for Sound Absorption and Transmission Control" (2005). Publications of the Ray W. HerrickLaboratories. Paper 50.http://docs.lib.purdue.edu/herrick/50
Porous Materials for Sound Absorption and Transmission
ControlControl
J. Stuart BoltonRay W. Herrick Laboratories
P d U i itPurdue University
Introduction
What are Porous Media? Two phases Two phases
Solid Fluid
Wh t d th d ? What do they do? Convert organized acoustical motion into heat
Dissipation of Energy
What don’t they do? Bl k d i t ll f l b i
Dissipation of Energy
Block sound : i.e., not usually useful as barriers(by themselves)
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Introduction
Dissipation mechanisms Viscous Viscous Thermal Structural
Examples of porous materials Glass fiber Mineral wool Mineral wool Open or partially open cell foams
Applications Automotive, Aircraft, …
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SEM – Glass Fiber
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SEM – Resinated Glass Fiber
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SEM – Partially Reticulated Foam
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SEM – Shoddy
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SEM – Thinsulate
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Sound Propagation in Porous Media
P M t i l Porous Materials
Two phases: Solid (frame) and gas (air) Allow two longitudinal wave types which appear in
both phases Allow transverse wave motion if frame possesses p
shear stiffness Display large sensitivity to boundary conditions if
frame is relatively stiff (modulus near that of air)
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Transmission Measurements
Test signal: Linear Frequency Sweep 0 Hz 25Frequency Sweep, 0 Hz-25 kHz, 20 ms
Sample Rate: 100 kHz Resolution: 12 bits Post-Acquisition: Re-
sample to 50 kHz
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Foam Impulse Response
Note: Frame Wave- first arrival
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Absorption treatments
Bonded/Bonded membranefoam
Bonded/Unbonded
backing
Unbonded/Bonded
airspace
Unbonded/Unbonded
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Normal Incidence AbsorptionEffects of Airspace at front and rear
1. Film/Foam/Backing 2. Film/Space/Foam/Backing3 Fil /F /S /B ki3. Film/Foam/Space/Backing4. Film/Space/Foam/Space/Backing
Foam – 25 mm, 30kg/m3
MembraneMembrane – 0.045 kg/m2
Airspaces – 1 mm
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Ch t i ti f P M diCharacterization of Porous Media
Rigid
Solid phase does not move Solid phase does not move Frame bulk modulus significantly greater than that of air Airborne wave only
*situations in which frame is not excited directly Porous ceramics Sintered metals
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Ch t i ti f P M diCharacterization of Porous Media
Limp
Solid phase moves – driven by fluid motion onlySolid phase moves – driven by fluid motion onlyFrame bulk modulus significantly less than of airAirborne wave onlyLimp glass fibers, thinsulate and other fibrous media
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Ch t i ti f P M diCharacterization of Porous Media
Elastic
Solid phase movesSolid phase movesFrame bulk modulus of same order of that as airAirborne, frame and shear wavesB d diti i t tBoundary conditions are very importantPolyurethane and polyimide foams
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Physical Properties of Porous Media
Acoustical properties are determined by macroscopicphysical properties.p y p p
- Flow resistivity- porosity Fluid-acoustical
t
gid
p - pore tortuosity- Bulk density- In vacuo bulk modulus
Sh d l
parametersRi
Lim
p
Ela
stic
- Shear modulus- Loss factor
With knowledge of these properties the acoustical
Elastic properties
E
With knowledge of these properties the acoustical performance of porous media can be predicted.
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Physical Properties of Porous Media
Flow Resistivity
Resistance to steady state flow through a porous material
Determined by- pore tortuosity- viscous drag
When pores are “straight”, measure of viscous dissipation potential
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Measurement of Physical Properties- Flow Resistivity
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Physical Properties of Porous Media
Tortuosity
M f d i ti f f t i ht li th h Measure of deviation of pore from straight line through material
Ratio of actual path length through material to linear path lengthpath length
Results in inertial coupling between solid and fluids phases
Ranges from 1 (low density fibrous material) to 10 Ranges from 1 (low density fibrous material) to 10 (partially reticulated foam)
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Modeling of Porous Media Objective Material
Microstructure
MacroscopicProperties
Limited
FundamentalAcoustic
Well Developed
Properties
Installed
Analytical Well Developed
Numerical Initial Work
InstalledAcoustic
Properties
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Microstructure to Macrostructure For fibrous media made up of mono-diameter fibers
(e.g., from Beranek, Noise and Vibration Control)
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Modeling of Porous MediaApproach followed by Bolton and Allard Based on theory of elastic porous materials by Biot (1956):
Allo s trans erse a e motion- Allows transverse wave motion- Expressed in very general form- Most widely used in geophysics
H Here:- Adapt theory to “acoustic” porous materials (i.e., foam and glass fiber)- Express in terms of conventional variables (i.e., displacement and
pressures)pressures)- Derive boundary conditions applicable to typical reflection and
transmission problems Results: Results:
- First theory capable of predicting oblique incidence behavior of foam in noise control application
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Theoretical Approach WRITE:
- stress-strain relations for each phase- stress strain relations for each phase- Dynamic relations for each phase
COMBINE TO YIELD TWO WAVE EQUATIONS:V l t i t i- Volumetric strain
- Rotational strain FROM SOLUTIONS DERIVE:
- Displacement fields- Normal and shear stresses at boundaries
DETERMINE COMPONENT AMPLITUDES: DETERMINE COMPONENT AMPLITUDES:- By application of boundary conditions
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Notation
Forces acting on solid phase/unit material area:
Forces acting on fluid phase/unit material area:
1. s = - hP, where h=porosity2. Solid displacement denoted by ū3. Fluid displacement denoted by Ū
* Notes:
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The RAYLEIGH Model
The original model The modified model (allowing f t t it )for pore tortuosity)
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Fluid-Structural Coupling Inertial – proportional to relative acceleration
Viscous – proportional to relative velocity
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Dynamic Relations
)()()1( 2
22
22
2
1 yyyyyxyy Uu
tbUu
tq
tu
xy
Solid:yyyy tttxy
)()()1(2
22
y uUbuUqUs
Fluid: )()()1( 2222 yyyy uU
tbuU
tq
ty
where = bulk density of framewhere ρ1= bulk density of frameρ2=ρ0h (bulk fluid density)q2 = structure factor (inertial coupling)q structure factor (inertial coupling)b = viscous coupling factor
* Note : Viscous and inertial coupling
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Wave Equations
Volumetric Strains: 024 BeeAe
Solution of form: xjkCe 2,1
Where:
242
22,1
BAAk
Note: two longitudinal wave types distinguished by different wave numbers: i.e.,
2
Airborne wave Frame wave
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Wave Equations
Rotational Strains: 022 tk Rotational Strains:
Solution of form: xjktCe
0 ztz k
Where: ωz = z-component of
Ce
kt = transverse wave wave number
Note: single transverse wave typeNote: single transverse wave type
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Phase Speed and Attenuation
Phase Speed Attenuation
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Forms of Solutions
xjkyjkyjkyjkyjk xyyyy eeCeCeCeCe ][ 22114321
xjkyjkyjk xtyty eeCeC ][ 6 z eeCeC ][ 65
222,12,1 xyy kkk 22
xtty kkk where: and
xyxxxyxx tltltltlz UUUUuuuu ,,,,,,,,,
xyy s ,,Then derive:
and
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Forms of Solutions Solid Displacement:
11 kk yjkyyjkyxjk
221
112
1
1 11 Cek
Cek
jeu yjkyyjkyxjky
yyx
22 kk jkjk
Longitudinal
422
232
2
2 22 Cekk
Cekk yjkyyjky yy
k yjkyjkxjk
t
x tytyx eCeCekkj 652 Transverse
Similar expression for U σ τ etc all in terms of six unknownSimilar expression for Uy,σy,τxy, etc., all in terms of six unknown constants C1-C6; they are determined by application of the boundary conditions.
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Sound Transmission Through Double Panels
Approach: Substitute allowed solutions into boundary conditions. Arrange as matrix problem in wave amplitudes and
solve for required coefficients.
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Boundary Conditions Open Surface:
1. Volume Velocity: vy = iω [ (1-h) uy + h Uy ]2. Fluid Force: - h p = sp3. Solid Force: - (1-h) p = σy
4. Shear Force: τxy = 0
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Boundary Conditions Bounded Euler-Bernoulli Plate (D, ms):
1. Normal Velocity: vy = iω W2. Solid Displacement: uy = W3 Fluid Displacement: U = W3. Fluid Displacement: Uy W4. Tangential Displacement: ux = - (h1/2) ∂W/∂x
5. Eqn. of Motion: hpsWmWD xy
)( 1
24
Note: 1. transverse wave excitation through 2-5.2. plate thickness affects coupling.
xps
tm
xD ys
2
)(24
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2. plate thickness affects coupling.
Absorption treatments
Bonded/Bonded membranefoam
Bonded/Unbonded
backing
Unbonded/Bonded
airspace
Unbonded/Unbonded
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Normal Incidence AbsorptionEffects of Airspace at front and rear
1. Film/Foam/Backing 2. Film/Space/Foam/Backing3 Fil /F /S /B ki3. Film/Foam/Space/Backing4. Film/Space/Foam/Space/Backing
Foam – 25 mm, 30kg/m3
MembraneMembrane – 0.045 kg/m2
Airspaces – 1 mm
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Sound Absorption Treatments
Owing to high impedance frame waves
1. “Loose” surface membrane yields better overall sound absorption than bonded membrane (with exception of very low frequencies)very low frequencies).
2. Small airspace (~ 1 mm) behind foam layer enhances low frequency performance with or without front membrane.
3. Light, loose membrane on foam with thin backing space gives performance as good as unfaced foamspace gives performance as good as unfaced foam while protecting foam.
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Sound Transmission Through Double Panels
Approach:Approach: Substitute allowed solutions into boundary conditions. Arrange as matrix problem in wave amplitudes and solve
for required coefficientsfor required coefficients
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Transmission Loss Measurements
Procedure Procedure
- Measure 1/3 octave mean square pressure in source room ( Ii )source room ( Ii )- Measure 1/3 octave transmitted intensity averaged over panel area ( It )( It )- TL = 10 log ( Ii / It )
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Test Panel Mounting
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Foam Mounting
• Note: Panel Dimensions – 1.2 m by 1.2 m
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Panel Configurations Tested
Foam:30 kg/m3 – 26 mm thick
Panel: Panel:Aluminum – 0.05” and 0.03” thick
Panel Separation:26 mm to 41 mm
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Transmission LossTheory
Experiment Double Panel: Lined - 0.05” & 0.03”
• Foam UNBONDED to incident side panel
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p
Transmission LossTheory
Experiment Double Panel: Lined - 0.03” & 0.05”
• Foam BONDED to both panels
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p
Transmission Loss Double Panel: Lined - 0.03” & 0.05”
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Sound Transmission
High impedance frame wave causes performance to depend on mountingto depend on mounting.
Avoid direct excitation of frame waves- do not continuously bond foam to backing- do not continuously bond surface treatments to foamfoam
Bonded attachmentShifts “mass-air-mass” resonance to higher frequencies- Shifts mass-air-mass resonance to higher frequencies
- Decreases high frequency transmission loss
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Multi-layer models and GUI program
• Develop various combinations of iso. or aniso. foam, stiff panel and air layers. • Implement user-friendly program running as GUI form.
O i iOrganizing by GUI
Aircraft Application
Conventional ribbed-aluminum fuselage Y
Honeycomb core• Different stiffness in X,Y & Z dir.• solid and fluid (air) parts
X
Replaced by
Z
Transversely poro-elastic modeling
Replaced by Nomex honeycomb sandwich Panel Y
• Transversely isotropic properties5 elastic constants : Ex = Ey , Ez ,Gzx ,v xy ,v zx
X
Z
y y
• Porous foam with constants, porosity, bulk density, flow resistivity and tortuosity
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TL for 1/2” lined and unlinedFuselage Example
Lined model 80
Lined with 1/2” glass fiber
prediction
measurement60
70
TL(dB)U li d
Unlined model
measurement
40
50
(dB)Unlined- 1/2” air layer
prediction
measurement
20
30
measurement
102 103 1040
10
Frequency (Hz)* About 15dB improvement above 1kHz by lining with ½” fibrous material in the i b t h b l Frequency (Hz)air space between honeycomb panel
and the interior trim.
Finite Element Modeling Practical Treatments
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Shape Optimization of Foam Wedge Objective – maximize absorption offered by a wedge
over a specified frequency rangeconstrained edgesrigid piston
f oamair
uo ejt a
hard wallc d
L
xy
- Wedge defined by θ when volume and a is held constant- Given volume find optimum angle, θ
L
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p g ,
Shape Optimization of Foam Wedge
0.8 0.
1.0 1.(a)
0.8 0
1.0(b)
0.4 0.4
0.6 0.
= 36o (optimal wedge)
0.4 0
0.6 0
0.0 0.
0.2 0.2
0 500 1000 1500 2000
( p g )
Frequency (Hz)
= 132o
= 180o
0.0 0
0.2 0
16 28 36 41 48 59 74 97 132 180wedge tip angle ()
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System Configurations
- In system (b), tortuosity of a foam layer is varied spatially across the duct (in y-direction).
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( y )
Sound Transmission Through A Wedge
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Sound Transmission Through A Foam Layer Having Spatially Graded Tortuosity
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Experimental Setup High Frequency Tube
B & K Type 3560Pulse System
B & K Type 3560Pulse System
B & K Type 3560Pulse System
B & K Type 3560Pulse System
B & K Type 3560Pulse System
B & K Type 3560Pulse Systemy
(Four Channel)y
(Four Channel)y
(Four Channel)y
(Four Channel)y
(Four Channel)y
(Four Channel)
2.9 cm361.9mKg
Signal AmplifierSignal
GeneratorSignal AmplifierSignal
GeneratorSignal AmplifierSignal
GeneratorSignal AmplifierSignal
GeneratorSignal AmplifierSignal
GeneratorSignal AmplifierSignal
GeneratorSignal AmplifierSignal
GeneratorSignal AmplifierSignal
Generator
A i ti d l fib
7.5 cmMicrophonesMicrophones 134 2MicrophonesMicrophonesMicrophonesMicrophones 134 2MicrophonesMicrophones
Aviation grade glass fiber
AnechoicTermination
AnechoicTermination
AnechoicTermination
AnechoicTermination
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
NewSampleHolderSampleHolderSampleHolderSampleHolderSampleHolder
AnechoicTermination
AnechoicTermination
AnechoicTermination
AnechoicTermination
AnechoicTermination
AnechoicTermination
AnechoicTermination
AnechoicTermination
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
NewSampleHolderSampleHolderSampleHolderSampleHolderSampleHolder
NewSampleHolder
NewSampleHolderSampleHolderSampleHolderSampleHolderSampleHolder
AnechoicTermination
AnechoicTermination
Purdue University Herrick Laboratories
B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206
Anechoic Transmission Loss
35
40Experiment Prediction using FEM (with edge constraint)Prediction without edge constraint
25
30
Prediction without edge constraint
15
20
TL (d
B)
5
10Increase in TLdue to edge constraint
102 103 1040
Frequency (Hz)
Shearing modeconstraint
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Constrained around Edge (50 Hz - 1600 Hz)
35
40ExperimentFEM
25
30
35
15
20
25
TL (d
B)
5
10
15
130 Hz280 Hz
102 1030
5
Frequency (Hz)
Purdue University Herrick Laboratories
Laser Measurement Setup (Large Tube 1” Sample A)(Large Tube, 1 Sample A)
xx
Computer
B & K Type 3560Pulse System(Four Channel) ComputerComputer
B & K Type 3560Pulse System(Four Channel) ComputerComputer
B & K Type 3560Pulse System(Four Channel) ComputerComputer
B & K Type 3560Pulse System(Four Channel) ComputerComputer
B & K Type 3560Pulse System(Four Channel) ComputerComputer
B & K Type 3560Pulse System(Four Channel) Computer
d
A
B
d
A
B
Signal AmplifierSignal Signal AmplifierSignal Signal AmplifierSignal Signal AmplifierSignalPolytec FiberOFV 3000C t ll
Signal AmplifierSignal Signal AmplifierSignal Signal AmplifierSignal Signal AmplifierSignalPolytec FiberOFV 3000C t ll
Signal AmplifierSignal Signal AmplifierSignal Signal AmplifierSignal Signal AmplifierSignalPolytec FiberOFV 3000C t ll
x2
x1
x2
x1
gGenerator
gGenerator
gGenerator
gGenerator
Sample
Controller
Polytec FiberOFV 511
Fiber interferometer123
gGenerator
gGenerator
gGenerator
gGenerator
Sample
Controller
Polytec FiberOFV 511
Fiber interferometer
gGenerator
gGenerator
gGenerator
gGenerator
Sample
Controller
Polytec FiberOFV 511
Fiber interferometer123
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Plexiglass Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Plexiglass Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Two-MicrophoneImpedance Measurement Tube
B & K Type 4206
Plexiglass
Purdue University Herrick Laboratories
The 1st and 2nd Mode Shapes of the Edge-constrained Sample (1”)
1
(a)
ax1
(b)
ax
Edge constrained Sample (1 )FEM Experiment
0.050
0.050
0.5
|vf/p
|/|vf
/p|m
a
0.050
0.050
0.5
|vf/p
|/|vf
/p|m
a
1st Modeat 100 Hz
(c) (d)
-0.05
0
-0.05
0
xy -0.05
0
-0.05
0
xy
at 100 Hz
0.050
0.5
1
|vf/p
|/|vf
/p|m
ax
0.050
0.5
1
|vf/p
|/|vf
/p|m
ax2nd Mode
-0.05
0
0.05
-0.05
0
xy -0.05
0
0.05
-0.05
0
xy
2nd Modeat 350 Hz
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Summary
Three types of porous media: rigid, limp and elasticW ti b d l d t l i Wave propagation can be modeled accurately using Biot theory and later variants
Given values for macroscopic parameters, acoustical p p ,behavior of sound absorbing materials can be accurately predicted
Foam finite elements can be used to model arbitrarily Foam finite elements can be used to model arbitrarily-shaped treatments
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Future Challenges
Anisotropy – all noise control materials are anisotropicI h it ll i t l t i l Inhomogeneity – all noise control materials are inhomogeneous
Nonlinearity – all noise control materials are nonlineary Inhomogeneous treatments – spatially distributed
properties to improve dissipation Material optimization – especially foams and fibrous
materials Addition of tuned elements to fibersAddition of tuned elements to fibers SEA compatible models
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