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

7-1-2013

The Influence of Boundary Conditions andConstraints on the Performance of Noise ControlTreatments: Foams to MetamaterialsJ Stuart BoltonPurdue University, [email protected]

Follow this and additional works at: http://docs.lib.purdue.edu/herrick

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Bolton, J Stuart, "The Influence of Boundary Conditions and Constraints on the Performance of Noise Control Treatments: Foams toMetamaterials" (2013). Publications of the Ray W. Herrick Laboratories. Paper 82.http://docs.lib.purdue.edu/herrick/82

J. Stuart BoltonRay. W. Herrick LaboratoriesSchool of Mechanical EngineeringPurdue University

RASD 2013, Pisa, Italy, July, 2013

Effect of front and rear surface boundary conditions on foam sound absorption

Influence of edge constraints on transmission loss of poroelastic materials including effect of finite mass supportssupports

Metamaterial Barrier

2

3

Normal Incidence Measurement Normal Incidence Measurement f flf flof Reflectionof Reflection

4

FilmFilm--faced Polyurethane Foamfaced Polyurethane Foam

Scanning electron micrographs of the foam sample

25mmlayeroffoam onesidecoveredwithflamebondedfilm,theotheropen.

Many intact membranesManyintactmembranes

5

Reflection Impulse ResponseReflection Impulse Response

(Film-faced surface up) (Foam-open surface up)

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OneOne--Dimensional Dimensional PoroelasticPoroelasticM i l ThM i l ThMaterial TheoryMaterial Theory

Equationsofmotion:Fluid:

Solid:

Based on Zwikker and Kosten, plus Rosin with complex density and air ff k f b hstiffness taken from Attenborough.

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Boundary ConditionsBoundary Conditions

Open foam surface Foam surface sealed with an i i b

Foam fixed to a hard backingimperious membrane

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Reflection Impulse Response Reflection Impulse Response --p pp pPredictedPredicted

Film-faced FoamOpen Surface Foam

Reflectionfromrearsurface Disaster!

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FilmFilm--faced Foam / Thin Air Gapfaced Foam / Thin Air Gap/ p/ p

Impedance:

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FilmFilm--forced Foam / Thin Air Gapforced Foam / Thin Air GapFilmFilm forced Foam / Thin Air Gapforced Foam / Thin Air Gap

1600 Hz350 Hz

1600 Hz

Inverted reflection from rear surface

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Rear Surface Boundary ConditionsRear Surface Boundary Conditions25mm foam layer with bonded membrane

1. No Airspace:

2. Airspace:p

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membranefoamo Bonded/Bondedbacking

/

o Bonded/Unbondedairspace

o Bonded/Unbonded

b d d d do Unbonded/Bonded

o Unbonded/Unbonded

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Normal Incidence AbsorptionNormal Incidence Absorptionpp

o Foam 25mm,30kg/m3o Membrane 0.045kg/m2o Airspaces 1mm

Effects of Airspace at front and rear

1.Film/Foam/Backing

2.Film/Space/Foam/Backing

3.Film/Foam/Space/Backing

EffectsofAirspaceatfrontandrear

/ / p / g

4.Film/Space/Foam/Space/Backing

14

Impedance Tube TestingImpedance Tube TestingMelamineFoam(8.6kg/m3)

100 mm diameter

p gp g

100mmdiameter 25mmthick

Eachsamplefitexactlybytrimmingthediameter&checkingthep y y g gfitwithaTLmeasurement

TwoFacing&TwoRearSurfaceBoundaryConditions Multipletrials Multiplesamples

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Sample Fit: TL QualificationSample Fit: TL Qualificationp Qp Q

N Z TL S l

Transmission Loss NonZeroTL=SampleConstrained AsCut

1st Trim

2nd Trim

3rd Trim

ZeroTL=SampleFreetoMove 4

th Trim

NoLeakage

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Surface ConfigurationsSurface ConfigurationsFront Surface: Rear Surface:

gg

1 2 1 2

Loose Glued Gap Fixed

1) Plastic film near, but not adhered to foam

1) Small gap between foam & rigid wall

) dh d d2) Plastic film glued to foam

2) Foam adhered to rigid wall

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Absorption vs. Configuration Absorption vs. Configuration -- TestTest

AbsorptionCoefficient Loose - Gap

-- TestTest

Loose - Fixed

Gl d GGlued - Gap

Glued-Fixed

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Helmholtz Resonator EffectHelmholtz Resonator Effect

??

M h i l I dMechanical Impedance

Mass

StiffStiffness

Total Acoustic Impedance

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Helmholtz Resonator EffectHelmholtz Resonator Effect

??

Combined Foam + Helmholtz Resonator System is Similar to

Measured System

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Helmholtz Resonator EffectHelmholtz Resonator Effect

??But is it really due to edge gaps?

Measured GluedF i Fi dFacing + Fixed

with Edge Sealed

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RestingonFloor BondedtoBacking

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Tensioned Tensioned MembranesMembranesModelModel VerificationVerification Velocity MeasurementVelocity MeasurementModel Model Verification Verification Velocity MeasurementVelocity Measurement

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Model Verification Model Verification Vibrational Vibrational ModesModesModesModes

Theory ExperimentAbsolute velocity of membrane - Experiment

1st 0.5

1

p

|

/

|

v

/

p

|

m

a

x

-0.050

0.05

-0.050

0.050

xy

|

v

/

2nd

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Model Verification Model Verification Experiment Experiment SetSet--upupSetSet--upup

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Model Verification Model Verification Model Model OptimizationOptimizationOptimizationOptimizationo Given experimental results as

input Find appropriate materialinput, Find appropriate material properties (To , s , )

Why this behavior? Finite size, held at edge, finite stiffness.

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Glass Fiber Material Inside of Glass Fiber Material Inside of Sample HolderSample HolderSample HolderSample Holder

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Anechoic Transmission Loss Anechoic Transmission Loss (Green)(Green)(Green)(Green)

35

40Experiment FE Prediction (Edge constrained)Prediction (Unconstrained case)

25

30

15

20

T

L

(

d

B

)

5

10

15

Increase in TL due to edge constraint

102 103 1040

5

F (H )

(10dB)Shearing mode

Frequency (Hz)

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PoroelasticPoroelastic Material Properties Material Properties Used in CalculationsUsed in CalculationsUsed in Calculations Used in Calculations

MaterialBulk

density

(Kg/m3)

Porosity TortuosityEstimated flow

resistivity

(MKS Rayls/m)

Shear modulus

(Pa)

Loss factor

Yellow

Green

6.7

9.6

0.99

0.99

1.1

1.1

21000

31000

1200

2800

0.350

0.275

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Variation of Shear ModulusVariation of Shear Moduluso As shear modulus increases, the minimum location of TL moves to

higher frequencies

30

35

40Shear M odulus = 1000 PaShear M odulus = 2000 PaShear M odulus = 3000 PaShear M odulus = 4000 Pa

20

25

30

L

(

d

B

)

10

15

T

L

102 103 1040

5

Frequency (Hz)Frequency (Hz)

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Variation of Flow ResistivityVariation of Flow Resistivity

40

FlowresistivitycontrolsTLatlowandhighfrequencylimit

30

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F low res is t ivity = 10000 M K S R ay ls /mF low res is t ivity = 20000 M K S R ay ls /mF low res is t ivity = 30000 M K S R ay ls /mF low res is t ivity = 40000 M K S R ay ls /m

20

25

T

L

(

d

B

)

1 0

15

10 2 10 3 10 40

5

F requenc y (H z )

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Investigation of Vibrational Investigation of Vibrational Modes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber Materials

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Vibrational Modes of Fiber Glass Vibrational Modes of Fiber Glass Materials (1st and 2nd Modes Green)Materials (1st and 2nd Modes Green)Materials (1st and 2nd Modes, Green)Materials (1st and 2nd Modes, Green)

ExperimentFEM

0

0.5

1

(a)

|

v

f

/

p

|

/

|

v

f

/

p

|

m

a

x

0

0.5

1

(b)

|

v

f

/

p

|

/

|

v

f

/

p

|

m

a

x

1st

-0.05

0

0.05

-0.05

0

0.050

xy -0.05

0

0.05

-0.05

0

0.050

xy

(133Hz)

0.5

1

(c)

|

/

|

v

f

/

p

|

m

a

x

0.5

1

(d)|

/

|

v

f

/

p

|

m

a

x

2nd

-0.05

0

0.05

-0.05

0

0.050

xy

|

v

f

/

p

|

-0.05

0

0.05

-0.05

0

0.050

xy

|

v

f

/

p

|2nd

(422Hz)

35

Internal Constraint to Enhance Internal Constraint to Enhance the Sound Transmission Lossthe Sound Transmission Lossthe Sound Transmission Loss the Sound Transmission Loss

36

Sound Tra