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Purdue University
Purdue e-Pubs Publications of the Ray W. Herrick Laboratories
School of Mechanical Engineering
7-1-2013
The Influence of Boundary Conditions and Constraints on the Performance of Noise Control Treatments: Foams to Metamaterials J Stuart Bolton Purdue University, [email protected]
Follow this and additional works at: http://docs.lib.purdue.edu/herrick Bolton, J Stuart, "The Influence of Boundary Conditions and Constraints on the Performance of Noise Control Treatments: Foams to Metamaterials" (2013). Publications of the Ray W. Herrick Laboratories. Paper 82. http://docs.lib.purdue.edu/herrick/82
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information.
J. Stuart Bolton Ray. W. Herrick Laboratories School of Mechanical Engineering Purdue 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 supports “Metamaterial” Barrier
2
3
Normal Incidence Measurement fl off Reflection
4
FilmFilm -faced 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 membranes Many intact membranes
5
Reflection Impulse Response
(Film-faced surface up)
(Foam-open surface up)
6
One-Dimensional Poroelastic OneM i l Th Material Theory
Equations of motion: Fluid: Solid: Based on Zwikker and Kosten, plus Rosin with complex density and air stiffness ff taken k from f Attenborough. b h 7
Boundary Conditions
Open foam surface
Foam surface sealed with an iimperious i b membrane
Foam fixed to a hard backing
8
Reflection Impulse p Response p Predicted Open Surface Foam
Reflection from rear surface
Film-faced Foam
Disaster!
9
FilmFilm -faced Foam / Thin Air Gap p
Impedance:
10
Film-forced Foam / Thin Air Gap FilmInverted reflection from rear surface
350 Hz
1600 Hz
11
Rear Surface Boundary Conditions 25mm foam layer with bonded membrane 1.
No Airspace:
2.
Airspace: p
12
/ o Bonded/Bonded
o Bonded/Unbonded
membrane foam backing
airspace
o Unbonded/Bonded b d d d d
o Unbonded/Unbonded
13
Normal Incidence Absorption p
– 25 mm, 30kg/m3
o
Foam
o
Membrane – 0.045 kg/m2
o
Airspaces
– 1 mm
Effects of Airspace at front and rear Effects of Airspace at front and rear 1. Film/Foam/Backing 2. Film/Space/Foam/Backing 3. Film/Foam/Space/Backing / / p / g 4. Film/Space/Foam/Space/Backing 14
Impedance p Tube Testing g Melamine Foam (8.6 kg/m3) 100 mm diameter 100 mm diameter 25 mm thick
Each sample fit exactly by trimming the diameter & checking the p y y g g fit with a TL measurement Two Facing & Two Rear Surface Boundary Conditions Multiple trials Multiple samples
15
Sample p Fit: TL Q Qualification Transmission Loss Non‐Zero TL = Sample N Z TL S l Constrained
As‐Cut 1st Trim 2nd Trim 3rd Trim
Zero TL = Sample Free to Move
4th Trim
No Leakage
16
Surface Configurations g Front Surface:
Rear Surface:
1
2
1
2
Loose
Glued
Gap
Fixed
1) Plastic film near, but not adhered to foam
1) Small gap between foam & rigid wall
2) Plastic film glued to foam
dh d to rigid d 2)) Foam adhered wall
17
Absorption vs. Configuration - Test Absorption Coefficient
Loose - Gap
Loose - Fixed
Gl d - Gap Glued G
Glued-Fixed
18
Helmholtz Resonator Effect
?
M h i l IImpedance Mechanical d Mass Stiffness Stiff Total Acoustic Impedance
19
Helmholtz Resonator Effect
?
Combined Foam + Helmholtz Resonator System is Similar to Measured System
20
Helmholtz Resonator Effect
? But is it really due to edge gaps?
Measured Glued F i + Fi Facing Fixed d with Edge Sealed
21
22
Resting on Floor
Bonded to Backing
23
Tensioned Membranes Model Verification – Velocity Measurement
25
Model Verification – Vibrational Modes Theory
Experiment
1st
|v/ p|/|v/p|max
Absolute velocity of membrane - Experiment 1 0.5
0 0.05 0
0.05 0
y -0.05 -0.05 x
2nd
26
Model Verification – Experiment SetSet -up
27
Model Verification – Model Optimization o Given experimental results as input Find appropriate material input, properties (To , ρs , η )
Why this behavior? – Finite size, held at edge, finite stiffness.
28
Glass Fiber Material Inside of Sample Holder
29
Anechoic Transmission Loss (Green) 40 35
Experiment FE Prediction (Edge constrained) Prediction (Unconstrained case)
30
TL (dB)
25 20 15
Increase in TL due to edge constraint (10dB)
10 5 0 2 10
Shearing mode 3
10 F Frequency (Hz) (H )
4
10
30
Poroelastic Material Properties Used in Calculations Material
Bulk density
Porosity
Tortuosity
(Kg/m3)
Estimated flow resistivity
Shear modulus
(MKS Rayls/m)
(Pa)
Loss factor
Yellow
6.7
0.99
1.1
21000
1200
0.350
Green
9.6
0.99
1.1
31000
2800
0.275
31
Variation of Shear Modulus o As shear modulus increases, the minimum location of TL moves to higher frequencies 40 35
S hear S hear S hear S hear
M odulus M odulus M odulus M odulus
= = = =
1000 2000 3000 4000
Pa Pa Pa Pa
30
TL L (dB)
25 20 15 10 5 0 2 10
3
10 F requenc y (Hz )
10
4
32
Variation of Flow Resistivity • Flow resistivity controls TL at low and high frequency limit 40 35
F lo w F lo w F lo w F lo w
re s is t ivit y re s is t ivit y re s is t ivit y re s is t ivit y
= = = =
10000 20000 30000 40000
MKS MKS MKS MKS
R a y ls / m R a y ls / m R a y ls / m R a y ls / m
30
TL (dB)
25 20 15 10 5 0 2 10
3
10 F re q u e n c y (H z )
10
4
33
Investigation of Vibrational Modes of Glass Fiber Materials
34
Vibrational Modes of Fiber Glass Materials (1st and 2nd Modes Modes, Green) FEM
Experiment
(133 Hz)
1
0.5
|vf/p|/|vf/p|max
1st
|vf/p|/|vf/p|max
1
(a)
0 0.05
0.5
(b)
0 0.05
0.05
0
0.05
0
0 y
-0.05
-0.05
0 y
x
(422 Hz)
-0.05
x
1
0.5
|vf/p||/|vf/p|max
2nd
|vf/p||/|vf/p|max
1
-0.05
(c)
0 0.05
0.5
(d)
0 0.05
0.05
0
0.05
0
0 y
-0.05
-0.05
x
0 y
-0.05
-0.05
x
35
Internal Constraint to Enhance the Sound Transmission Loss
36
Sound Transmission Loss (Experiment, Experiment Green) Green) [Density of Plexiglass Plexiglass:: 1717 Kg/m3]
37
Effect of Releasing the Internal CrossCross - Constraint (Measurement) 30
TL(dB)
25
Cardboard Constraint
20 15 10 5 0 10
2
10
3
40 35
(b )
30
TL (dB)
25 20
Plexiglass Constraint
15 10 5 0 10
2
10
3
F re q u e n c y (H z)
heavy constraint required to realize Relatively Relatively heavy constraint required to realize low frequency benefit. 38
Effect of Releasing the Internal CrossCross - Constraint (FEM Prediction) 30
Cardboard C db d Constraint
TL (dB)
25 20 15 10 5 0 10
2
10
3
40 35
(b )
30
TL (dB)
25
Plexiglass Constraint
20 15 10 5 0 10
2
10
3
F re q u e n c y (H z)
39
Metamaterials o 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 MassMass-Neutral Material Homogenized mat. Cellular panel
nL
Meff : Meff f ≡
T
2 0 c 2 0c j 2 fMeff f
STL 20log T Meff : Mass per unit area Frame (Mat. A)
STL : Sound Transmission Loss
Plate (Mat. B)
nL L L
Unit cell
Cellular material with a periodic array of unit cells Unit cell has components with contrasting mass and moduli of infinite, periodic panel are same as that Characteristics Characteristics of infinite, periodic panel are same as that of a unit cell for normally incident sound 42
Low 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 Apportioning Each unit cell Overall mass constant Different materials for frame and plate iff i l f f d l A series of cases for μ between 0.1 and 10000 ρp and ρ ρf varied Ef varied keeping Ep constant so that Ef E p f p Mat. A
Mat. B
Base unit cell
Cellular unit cell
44
Experimental Validation o A good qualitative agreement is observed between measurements and FE predictions
45
MaterialMaterial -Based Mass Apportioning pp 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 µ →O(100)→saturates →O(100)→ t t
Ep = 2 GPa 46
Effective Mass as a Function of Frequency Magnitude of Meff higher than space‐averaged areal mass in the range of 0‐1000 Hz An order of magnitude higher in 800 – A d f it d hi h i 800 1000 Hz range 1000 H Shows strong negative mass effect in the peak STL region T
2 0 c 2 0c j 2 fMeff f
47
Mechanism Behind High STL
o Averaged displacement phase switches from negative to positive positive value at the STL peak 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 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 Material Low Sound Speed Front
Directs non‐normally incident sound to core
Metamaterial Core
Locally resonant core
Fibrous Cell Filling
Fibrous cell filling g Increases STL at high Hz
o Predicted Sound Transmission Loss in Hybrid System with Fibrous Cell Filling
50
• Front and rear boundary conditions have a profound effect on the sound absorption offered by poroelastic offered 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 would constraints 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 y Schultz
Current Students: • Srinivas Varanasi • Yangfan Liu
52
•
pp. 3–11: J. Stuart Bolton, Ph.D. Thesis, University of Southampton, 1984. Cepstral pp 3 11: J Stuart Bolton Ph D Thesis University of Southampton 1984 Cepstral techniques in the 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 absorbers Michigan, 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 structures 485‐495, 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 America 80(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/
53
Purdue e-Pubs Publications of the Ray W. Herrick Laboratories
School of Mechanical Engineering
7-1-2013
The Influence of Boundary Conditions and Constraints on the Performance of Noise Control Treatments: Foams to Metamaterials J Stuart Bolton Purdue University, [email protected]
Follow this and additional works at: http://docs.lib.purdue.edu/herrick Bolton, J Stuart, "The Influence of Boundary Conditions and Constraints on the Performance of Noise Control Treatments: Foams to Metamaterials" (2013). Publications of the Ray W. Herrick Laboratories. Paper 82. http://docs.lib.purdue.edu/herrick/82
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information.
J. Stuart Bolton Ray. W. Herrick Laboratories School of Mechanical Engineering Purdue 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 supports “Metamaterial” Barrier
2
3
Normal Incidence Measurement fl off Reflection
4
FilmFilm -faced 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 membranes Many intact membranes
5
Reflection Impulse Response
(Film-faced surface up)
(Foam-open surface up)
6
One-Dimensional Poroelastic OneM i l Th Material Theory
Equations of motion: Fluid: Solid: Based on Zwikker and Kosten, plus Rosin with complex density and air stiffness ff taken k from f Attenborough. b h 7
Boundary Conditions
Open foam surface
Foam surface sealed with an iimperious i b membrane
Foam fixed to a hard backing
8
Reflection Impulse p Response p Predicted Open Surface Foam
Reflection from rear surface
Film-faced Foam
Disaster!
9
FilmFilm -faced Foam / Thin Air Gap p
Impedance:
10
Film-forced Foam / Thin Air Gap FilmInverted reflection from rear surface
350 Hz
1600 Hz
11
Rear Surface Boundary Conditions 25mm foam layer with bonded membrane 1.
No Airspace:
2.
Airspace: p
12
/ o Bonded/Bonded
o Bonded/Unbonded
membrane foam backing
airspace
o Unbonded/Bonded b d d d d
o Unbonded/Unbonded
13
Normal Incidence Absorption p
– 25 mm, 30kg/m3
o
Foam
o
Membrane – 0.045 kg/m2
o
Airspaces
– 1 mm
Effects of Airspace at front and rear Effects of Airspace at front and rear 1. Film/Foam/Backing 2. Film/Space/Foam/Backing 3. Film/Foam/Space/Backing / / p / g 4. Film/Space/Foam/Space/Backing 14
Impedance p Tube Testing g Melamine Foam (8.6 kg/m3) 100 mm diameter 100 mm diameter 25 mm thick
Each sample fit exactly by trimming the diameter & checking the p y y g g fit with a TL measurement Two Facing & Two Rear Surface Boundary Conditions Multiple trials Multiple samples
15
Sample p Fit: TL Q Qualification Transmission Loss Non‐Zero TL = Sample N Z TL S l Constrained
As‐Cut 1st Trim 2nd Trim 3rd Trim
Zero TL = Sample Free to Move
4th Trim
No Leakage
16
Surface Configurations g Front Surface:
Rear Surface:
1
2
1
2
Loose
Glued
Gap
Fixed
1) Plastic film near, but not adhered to foam
1) Small gap between foam & rigid wall
2) Plastic film glued to foam
dh d to rigid d 2)) Foam adhered wall
17
Absorption vs. Configuration - Test Absorption Coefficient
Loose - Gap
Loose - Fixed
Gl d - Gap Glued G
Glued-Fixed
18
Helmholtz Resonator Effect
?
M h i l IImpedance Mechanical d Mass Stiffness Stiff Total Acoustic Impedance
19
Helmholtz Resonator Effect
?
Combined Foam + Helmholtz Resonator System is Similar to Measured System
20
Helmholtz Resonator Effect
? But is it really due to edge gaps?
Measured Glued F i + Fi Facing Fixed d with Edge Sealed
21
22
Resting on Floor
Bonded to Backing
23
Tensioned Membranes Model Verification – Velocity Measurement
25
Model Verification – Vibrational Modes Theory
Experiment
1st
|v/ p|/|v/p|max
Absolute velocity of membrane - Experiment 1 0.5
0 0.05 0
0.05 0
y -0.05 -0.05 x
2nd
26
Model Verification – Experiment SetSet -up
27
Model Verification – Model Optimization o Given experimental results as input Find appropriate material input, properties (To , ρs , η )
Why this behavior? – Finite size, held at edge, finite stiffness.
28
Glass Fiber Material Inside of Sample Holder
29
Anechoic Transmission Loss (Green) 40 35
Experiment FE Prediction (Edge constrained) Prediction (Unconstrained case)
30
TL (dB)
25 20 15
Increase in TL due to edge constraint (10dB)
10 5 0 2 10
Shearing mode 3
10 F Frequency (Hz) (H )
4
10
30
Poroelastic Material Properties Used in Calculations Material
Bulk density
Porosity
Tortuosity
(Kg/m3)
Estimated flow resistivity
Shear modulus
(MKS Rayls/m)
(Pa)
Loss factor
Yellow
6.7
0.99
1.1
21000
1200
0.350
Green
9.6
0.99
1.1
31000
2800
0.275
31
Variation of Shear Modulus o As shear modulus increases, the minimum location of TL moves to higher frequencies 40 35
S hear S hear S hear S hear
M odulus M odulus M odulus M odulus
= = = =
1000 2000 3000 4000
Pa Pa Pa Pa
30
TL L (dB)
25 20 15 10 5 0 2 10
3
10 F requenc y (Hz )
10
4
32
Variation of Flow Resistivity • Flow resistivity controls TL at low and high frequency limit 40 35
F lo w F lo w F lo w F lo w
re s is t ivit y re s is t ivit y re s is t ivit y re s is t ivit y
= = = =
10000 20000 30000 40000
MKS MKS MKS MKS
R a y ls / m R a y ls / m R a y ls / m R a y ls / m
30
TL (dB)
25 20 15 10 5 0 2 10
3
10 F re q u e n c y (H z )
10
4
33
Investigation of Vibrational Modes of Glass Fiber Materials
34
Vibrational Modes of Fiber Glass Materials (1st and 2nd Modes Modes, Green) FEM
Experiment
(133 Hz)
1
0.5
|vf/p|/|vf/p|max
1st
|vf/p|/|vf/p|max
1
(a)
0 0.05
0.5
(b)
0 0.05
0.05
0
0.05
0
0 y
-0.05
-0.05
0 y
x
(422 Hz)
-0.05
x
1
0.5
|vf/p||/|vf/p|max
2nd
|vf/p||/|vf/p|max
1
-0.05
(c)
0 0.05
0.5
(d)
0 0.05
0.05
0
0.05
0
0 y
-0.05
-0.05
x
0 y
-0.05
-0.05
x
35
Internal Constraint to Enhance the Sound Transmission Loss
36
Sound Transmission Loss (Experiment, Experiment Green) Green) [Density of Plexiglass Plexiglass:: 1717 Kg/m3]
37
Effect of Releasing the Internal CrossCross - Constraint (Measurement) 30
TL(dB)
25
Cardboard Constraint
20 15 10 5 0 10
2
10
3
40 35
(b )
30
TL (dB)
25 20
Plexiglass Constraint
15 10 5 0 10
2
10
3
F re q u e n c y (H z)
heavy constraint required to realize Relatively Relatively heavy constraint required to realize low frequency benefit. 38
Effect of Releasing the Internal CrossCross - Constraint (FEM Prediction) 30
Cardboard C db d Constraint
TL (dB)
25 20 15 10 5 0 10
2
10
3
40 35
(b )
30
TL (dB)
25
Plexiglass Constraint
20 15 10 5 0 10
2
10
3
F re q u e n c y (H z)
39
Metamaterials o 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 MassMass-Neutral Material Homogenized mat. Cellular panel
nL
Meff : Meff f ≡
T
2 0 c 2 0c j 2 fMeff f
STL 20log T Meff : Mass per unit area Frame (Mat. A)
STL : Sound Transmission Loss
Plate (Mat. B)
nL L L
Unit cell
Cellular material with a periodic array of unit cells Unit cell has components with contrasting mass and moduli of infinite, periodic panel are same as that Characteristics Characteristics of infinite, periodic panel are same as that of a unit cell for normally incident sound 42
Low 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 Apportioning Each unit cell Overall mass constant Different materials for frame and plate iff i l f f d l A series of cases for μ between 0.1 and 10000 ρp and ρ ρf varied Ef varied keeping Ep constant so that Ef E p f p Mat. A
Mat. B
Base unit cell
Cellular unit cell
44
Experimental Validation o A good qualitative agreement is observed between measurements and FE predictions
45
MaterialMaterial -Based Mass Apportioning pp 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 µ →O(100)→saturates →O(100)→ t t
Ep = 2 GPa 46
Effective Mass as a Function of Frequency Magnitude of Meff higher than space‐averaged areal mass in the range of 0‐1000 Hz An order of magnitude higher in 800 – A d f it d hi h i 800 1000 Hz range 1000 H Shows strong negative mass effect in the peak STL region T
2 0 c 2 0c j 2 fMeff f
47
Mechanism Behind High STL
o Averaged displacement phase switches from negative to positive positive value at the STL peak 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 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 Material Low Sound Speed Front
Directs non‐normally incident sound to core
Metamaterial Core
Locally resonant core
Fibrous Cell Filling
Fibrous cell filling g Increases STL at high Hz
o Predicted Sound Transmission Loss in Hybrid System with Fibrous Cell Filling
50
• Front and rear boundary conditions have a profound effect on the sound absorption offered by poroelastic offered 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 would constraints 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 y Schultz
Current Students: • Srinivas Varanasi • Yangfan Liu
52
•
pp. 3–11: J. Stuart Bolton, Ph.D. Thesis, University of Southampton, 1984. Cepstral pp 3 11: J Stuart Bolton Ph D Thesis University of Southampton 1984 Cepstral techniques in the 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 absorbers Michigan, 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 structures 485‐495, 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 America 80(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/
53
