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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
• 25 mm layer of foam – one side covered with flame‐bonded film, the other open.
• Many intact membranesMany intact membranes
5
Reflection Impulse ResponseReflection Impulse Response
(Film-faced surface up) (Foam-open surface up)
6
OneOne--Dimensional Dimensional PoroelasticPoroelasticM i l ThM i l ThMaterial TheoryMaterial Theory
Equations of motion:Fluid:
Solid:
Based on Zwikker and Kosten, plus Rosin with complex density and air ff k f b hstiffness taken from Attenborough.
7
Boundary ConditionsBoundary Conditions
Open foam surface Foam surface sealed with an i i b
Foam fixed to a hard backingimperious membrane
8
Reflection Impulse Response Reflection Impulse Response --p pp pPredictedPredicted
Film-faced FoamOpen Surface Foam
Reflection from rear surface Disaster!
9
FilmFilm--faced Foam / Thin Air Gapfaced Foam / Thin Air Gap/ p/ p
Impedance:
10
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
11
Rear Surface Boundary ConditionsRear Surface Boundary Conditions25mm foam layer with bonded membrane
1. No Airspace:
2. Airspace:p
12
membranefoamo Bonded/Bondedbacking
/
o Bonded/Unbondedairspace
o Bonded/Unbonded
b d d d do Unbonded/Bonded
o Unbonded/Unbonded
13
Normal Incidence AbsorptionNormal Incidence Absorptionpp
o Foam – 25 mm, 30kg/m3
o Membrane – 0.045 kg/m2
o Airspaces – 1 mm
Effects of Airspace at front and rear
1. Film/Foam/Backing
2. Film/Space/Foam/Backing
3. Film/Foam/Space/Backing
Effects of Airspace at front and rear
/ / p / g
4. Film/Space/Foam/Space/Backing
14
Impedance Tube TestingImpedance Tube TestingMelamine Foam (8.6 kg/m3)
100 mm diameter
p gp g
100 mm diameter 25 mm thick
Each sample fit exactly by trimming the diameter & checking the p y y g gfit with a TL measurement
Two Facing & Two Rear Surface Boundary Conditions
Multiple trials Multiple samples
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Sample Fit: TL QualificationSample Fit: TL Qualificationp Qp Q
N Z TL S l
Transmission Loss
Non‐Zero TL = Sample Constrained As‐Cut
1st Trim
2nd Trim
3rd Trim
Zero TL = Sample Free to Move 4th Trim
No Leakage
16
Surface ConfigurationsSurface Configurations
Front 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
17
Absorption vs. Configuration Absorption vs. Configuration -- TestTest
Absorption Coefficient Loose - Gap
-- TestTest
Loose - Fixed
Gl d GGlued - Gap
Glued-Fixed
18
Helmholtz Resonator EffectHelmholtz Resonator Effect
??
M h i l I dMechanical Impedance
Mass
StiffStiffness
Total Acoustic Impedance
19
Helmholtz Resonator EffectHelmholtz Resonator Effect
??
Combined Foam + Helmholtz Resonator System is Similar to
Measured System
20
Helmholtz Resonator EffectHelmholtz Resonator Effect
??But is it really due to edge gaps?
Measured GluedF i Fi dFacing + Fixed
with Edge Sealed
21
22
Resting on Floor Bonded to Backing
23
Tensioned Tensioned MembranesMembranesModelModel VerificationVerification –– Velocity MeasurementVelocity MeasurementModel Model Verification Verification –– Velocity MeasurementVelocity Measurement
25
Model Verification Model Verification –– Vibrational Vibrational ModesModesModesModes
Theory ExperimentAbsolute velocity of membrane - Experiment
1st 0.5
1
p|/|v
/p|m
ax
-0.050
0.05
-0.050
0.050
xy
|v/
2nd
26
Model Verification Model Verification –– Experiment Experiment SetSet--upupSetSet--upup
27
Model Verification Model Verification –– Model Model OptimizationOptimizationOptimizationOptimization
o Given experimental results as input Find appropriate materialinput, Find appropriate material properties (To , ρs , η )
Why this behavior? – Finite size, held at edge, finite stiffness.
28
Glass Fiber Material Inside of Glass Fiber Material Inside of Sample HolderSample HolderSample HolderSample Holder
29
Anechoic Transmission Loss Anechoic Transmission Loss (Green)(Green)(Green)(Green)
35
40Experiment FE Prediction (Edge constrained)Prediction (Unconstrained case)
25
30
15
20
TL (d
B)
5
10
15
Increase in TL due to edge constraint
102 103 1040
5
F (H )
(10dB)Shearing mode
Frequency (Hz)
30
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
31
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
TL
102 103 1040
5
Frequency (Hz)Frequency (Hz)
32
Variation of Flow ResistivityVariation of Flow Resistivity
40
• Flow resistivity controls TL at low and high frequency limit
30
35
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
TL (d
B)
1 0
15
10 2 10 3 10 40
5
F requenc y (H z )
33
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)
|vf/p
|/|vf
/p|m
ax
0
0.5
1
(b)
|vf/p
|/|vf
/p|m
ax
1st
-0.05
0
0.05
-0.05
0
0.050
xy -0.05
0
0.05
-0.05
0
0.050
xy
(133 Hz)
0.5
1
(c)
|/|vf
/p|m
ax
0.5
1
(d)|/|
vf/p
|max
2nd
-0.05
0
0.05
-0.05
0
0.050
xy
|vf/p
|
-0.05
0
0.05
-0.05
0
0.050
xy
|vf/p
|2nd
(422 Hz)
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 Transmission Loss Sound Transmission Loss ((Experiment GreenExperiment Green)) [Density of[Density of PlexiglassPlexiglass: 1717 Kg/m3]: 1717 Kg/m3]((Experiment, GreenExperiment, Green)) [Density of [Density of PlexiglassPlexiglass: 1717 Kg/m3]: 1717 Kg/m3]
37
Effect of Releasing the Internal Effect of Releasing the Internal CrossCross-- Constraint (Measurement)Constraint (Measurement)CrossCross Constraint (Measurement)Constraint (Measurement)
Cardboard25
30
CardboardConstraint
5
10
15
20
TL(
dB)
30
35
40
(b)
102 1030
PlexiglassConstraint10
15
20
25
30
TL
(dB)
102 1030
5
F requenc y (H z)
Relatively heavy constraint required to realize Relatively heavy constraint required to realize low frequency benefit.
38
Effect of Releasing the Internal Effect of Releasing the Internal CrossCross Constraint (FEM Prediction)Constraint (FEM Prediction)CrossCross-- Constraint (FEM Prediction)Constraint (FEM Prediction)
30
C db d
5
10
15
20
25
TL
(dB)
CardboardConstraint
102 1030
5
35
40
(b)
15
20
25
30
TL
(dB) Plexiglass
Constraint
102 1030
5
10
F requenc y (H z)
39
MetamaterialsMetamaterialso Metamaterials are artificial materials engineered to have properties that may not be
found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior.composition, using small inhomogeneities to create effective macroscopic behavior.
From : Meta‐Material Sound Insulation by E. Wester, X. Bremaud and B. Smith, Building Acoustics, 16 (2009)
40
41
Proposed MassProposed Mass--Neutral MaterialNeutral MaterialHomogenized mat.
Cellular panel
MM f 2 cnL
≡
: fff fe eMM f
0
0
22 2
20logeff
cTc j f
STL
M f
T
Frame (Mat. A)
: Mass per unit area: Sound Transmission Loss
eff
STLM
Plate (Mat. B)
Unit cellnL L
LL Cellular material with a periodic array of unit cells
Unit cell has components with contrasting mass and moduli
Characteristics of infinite, periodic panel are same as that Characteristics of infinite, periodic panel are same as that of a unit cell for normally incident sound
42
Low Frequency EnhancementLow Frequency Enhancement
A clamped plate has high STL at very low frequencies due to the effect of boundary conditions and finite size and stiffness.
43
MaterialMaterial--Based Mass ApportioningBased Mass ApportioningMaterialMaterial Based Mass ApportioningBased Mass Apportioning Each unit cell
Overall mass constant iff i l f f d l Different materials for frame and plate
A series of cases for μ between 0.1 and 10000 ρp and ρf variedρp ρf Ef varied keeping Ep constant so that
Mat. A
f p f pE E
Mat. B
Base unit cell Cellular unit cellBase unit cell Cellular unit cell
44
Experimental ValidationExperimental Validationo A good qualitative agreement is observed
between measurements and FE predictions
45
MaterialMaterial--Based Mass ApportioningBased Mass Apportioningpp gpp g As µ↑
High STL region broadens in the low frequency regime
Region between the first peak and dip is widening Region between the first peak and dip is widening
The dip – being shifted to the right – desirable
→O(100)→ t t µ→O(100)→saturates
Ep = 2 GPa
46
Effective Mass as a Function of FrequencyEffective Mass as a Function of FrequencyEffective Mass as a Function of FrequencyEffective Mass as a Function of Frequency Magnitude of Meff higher than space‐averaged areal mass
in the range of 0‐1000 Hz
A d f it d hi h i 800 1000 H An order of magnitude higher in 800 – 1000 Hz range
Shows strong negative mass effect in the peak STL region
02 cT 02 2 effc j fM f
47
Mechanism Behind High STLMechanism Behind High STL
o Averaged displacement phase switches from negative to positive value at the STL peakpositive value at the STL peak
o Parts of the structure move in opposite directions—similar to observations in LRSMs—resulting in zero averaged displacement
o “Negative mass” observed without locally resonant elements
48
Hybrid MaterialHybrid Material
o Cellular structure increases STL at low frequencies
o Lightweight, fine fiber fibrous layer can be used to recover performance at higher frequencies
49
Hybrid MaterialHybrid MaterialLow Sound Speed Front Metamaterial Core Fibrous Cell Filling
Directs non‐normally Locally resonant core Fibrous cell fillingincident sound to core
Locally resonant core gIncreases STL at high Hz
o Predicted Sound Transmission Loss in Hybrid System with Fibrous Cell Filling
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• Front and rear boundary conditions have a profound effect on the sound absorption
offered by poroelastic materialsoffered by poroelastic materials
• Those effects are predictable and measureable
• Internal constraint of poroelastic materials can increase their transmission loss, but
finite weight of required supports should be accounted for
•Metamaterials for transmission loss typically depend on the presence of constraints,
geometry and flexural stiffness for their performance
• A proposed mass‐neutral “metamaterial” barrier featuring spatially‐periodic internal
constraints gives low frequency advantage with respect to the mass law but wouldconstraints gives low frequency advantage with respect to the mass law, but would
require supplementary material to mitigate performance loss at high frequencies
51
Former Students:• Edward R. Green
• Bryan H. Song
• Jinho Song
• Ryan Schultz
Current Students:y
• Srinivas Varanasi
• Yangfan Liu
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pp 3 11: J Stuart Bolton Ph D Thesis University of Southampton 1984 Cepstral techniques in the• pp. 3–11: J. Stuart Bolton, Ph.D. Thesis, University of Southampton, 1984. Cepstral techniques in the measurement of acoustic reflection coefficients, with applications to the determination of acoustic properties of elastic porous materials.
• pp. 12‐14: J. Stuart Bolton, Paper DD4 presented at 110th meeting of the Acoustical Society of America, Nashville TN, November 1985. Abstract published in the Journal of the Acoustical Society of America 78(S1) S60. Normal incidence absorption properties of single layers of elastic porous materials.
• pp. 15‐21: Ryan Schultz and J. Stuart Bolton, Proceedings of INTER‐NOISE 2012, New York City, 19‐22 August, 2012. Effect of solid phase properties on the acoustic performance of poroelastic materials.
• pp. 25‐28: Jinho Song and J. Stuart Bolton, Proceedings of INTER‐NOISE 2002, paper N574, 6 pages, Dearborn, Michigan August 2002 Modeling of membrane sound absorbersMichigan, August 2002. Modeling of membrane sound absorbers.
• pp. 29‐33: Bryan H. Song, J. Stuart Bolton and Yeon June Kang, Journal of the Acoustical Society of America, Vol. 110, 2902‐2916, 2001. Effect of circumferential edge constraint on the acoustical properties of glass fiber materials.
• pp. 34‐35: Bryan H. Song, and J. Stuart Bolton, Journal of the Acoustical Society of America, Vol. 113, 1833‐1849, 2003. Investigation of the vibrational modes of edge‐constrained fibrous samples placed in a standing wave tube.
• pp. 36‐39: Bryan H. Song and J. Stuart Bolton, Noise Control Engineering Journal, Vol. 51, 16‐35, 2003. Enhancement of the barrier performance of porous linings by using internal constraints.
• pp. 42‐49: Srinivas Varanasi, J. Stuart Bolton, Thomas Siegmund and Raymond J. Cipra, Applied Acoustics, Vol. 74, 485 495 2013 The low frequency performance of metamaterial barriers based on cellular structures485‐495, 2013. The low frequency performance of metamaterial barriers based on cellular structures.
• See also: J. Stuart Bolton and Edward R. Green, Paper E4 presented at 112th meeting of the Acoustical Society of America, Anaheim CA, December 1986. Abstract published in the Journal of the Acoustical Society of America80(S1), p. S10. Acoustic energy propagation in noise control foams: approximate formulae for surface normal impedance.
• Presentations available at: http://docs.lib.purdue.edu/herrick/
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