The efficient use of plastic foams in a diverse range of structural applications like in noise reduction, cushioning, and sleeping mattresses requires detailed characterization of their permeability and deformation (load-bearing) behavior. The elastic moduli and airflow resistance properties of foams are often measured using two separate techniques, one employing mechanical vibration methods and the other, flow rates of fluids based on fluid mechanics technology, respectively. A multi-parameter inverse acoustic scattering problem to recover airflow resistivity (AR) and mechanical properties of an air-saturated foam cylinder is solved. A wave-fluid saturated poroelastic structure interaction model based on the modified Biot theory and plane-wave decomposition using orthogonal cylindrical functions is employed to solve the inverse problem. The solutions to the inverse problem are obtained by constructing the objective functional given by the total square of the difference between predictions from the model and scattered acoustic field data acquired in an anechoic chamber. The value of the recovered AR is in good agreement with that of a slab sample cut from the cylinder and characterized using a method employing low frequency transmitted and reflected acoustic waves in a long waveguide developed by Fellah et al. [Rev. Sci. Instrum. 78(11), 114902 (2007)].

1.
J.-P.
Groby
,
E.
Ogam
,
L.
De Ryck
,
N.
Sebaa
, and
W.
Lauriks
, “
Analytical method for the ultrasonic characterization of homogeneous rigid porous materials from transmitted and reflected coefficients
,”
J. Acoust. Soc. Am.
127
(
2
),
764
772
(
2010
).
2.
E.
Ogam
,
Z. E. A.
Fellah
,
N.
Sebaa
, and
J.-P.
Groby
, “
Non-ambiguous recovery of Biot poroelastic parameters of cellular panels using ultrasonic waves
,”
J. Sound Vib.
330
(
6
),
1074
1090
(
2011
).
3.
N.
Sebaa
,
Z. E. A.
Fellah
,
M.
Fellah
,
E.
Ogam
,
A.
Wirgin
,
F. G.
Mitri
,
C.
Depollier
, and
W.
Lauriks
, “
Ultrasonic characterization of human cancellous bone using the Biot theory: Inverse problem
,”
J. Acoust. Soc. Am.
120
(
4
),
1816
1824
(
2006
).
4.
N. J.
Mills
, “
The wet Kelvin model for air flow through open-cell polyurethane foams
,”
J. Mater. Sci.
40
,
5851
5945
(
2005
).
5.
R. J.
Goldstein
,
Fluid Mechanics Measurements
(
Taylor and Francis
,
Philadelphia, PA
,
1996
), Chaps. 2 and 5.
6.
M.
Garai
and
F.
Pompoli
, “
A European inter-laboratory test of airflow resistivity measurements
,”
Acta Acust. Acust.
89
,
471
478
(
2003
).
7.
M. R.
Stinson
and
G. A.
Daigle
, “
Electronic system for the measurement of flow resistance
,”
J. Acoust. Soc. Am.
83
(
6
),
2422
2428
(
1988
).
8.
V.
Tarnow
, “
Measured anisotropic air flow resistivity and sound attenuation of glass wool
,”
J. Acoust. Soc. Am.
111
(
6
),
2735
2739
(
2002
).
9.
ISO 9053:1991, Acoustics—Materials for acoustical applications—Determination of airflow resistance (International Organization for Standardization, Geneva, Switzerland, 1991).
10.
M.
Etchessahar
,
S.
Sahraoui
,
L.
Benyahia
, and
J. F.
Tassin
, “
Frequency dependence of elastic properties of acoustic foams
,”
J. Acoust. Soc. Am.
117
(
3
),
1114
1121
(
2005
).
11.
T.
Pritz
, “
Dynamic Young's modulus and loss factor of plastic foams for impact sound isolation
,”
J. Sound Vib.
178
(
3
),
315
322
(
1994
).
12.
A.
Sfaoui
, “
On the viscoelasticity of the polyurethane foam
,”
J. Acoust. Soc. Am.
97
(
2
),
1046
1052
(
1995
).
13.
R.
Deng
,
P.
Davies
, and
A. K.
Bajaj
, “
Flexible polyurethane foam modelling and identification of viscoelastic parameters for automotive seating applications
,”
J. Sound Vib.
262
(
3
),
391
417
(
2003
).
14.
E.
Ogam
,
A.
Wirgin
,
S.
Schneider
,
Z. E. A.
Fellah
, and
Y.
Xu
, “
Recovery of elastic parameters of cellular materials by inversion of vibrational data
,”
J. Sound Vib.
313
(
3–5
),
525
543
(
2008
).
15.
J. Y.
Chung
and
D. A.
Blaser
, “
Transfer function method of measuring in-duct acoustic properties. I. Theory
,”
J. Acoust. Soc. Am.
68
(
3
),
907
913
(
1980
).
16.
N.
Kino
and
T.
Ueno
, “
Comparisons between characteristic lengths and fibre equivalent diameters in glass fibre and melamine foam materials of similar flow resistivity
,”
Appl. Acoust.
69
(
4
),
325
331
(
2008
).
17.
N.
Kino
,
T.
Ueno
,
Y.
Suzuki
, and
H.
Makino
, “
Investigation of non-acoustical parameters of compressed melamine foam materials
,”
Appl. Acoust.
70
(
4
),
595
604
(
2009
).
18.
O.
Doutres
,
Y.
Salissou
,
N.
Atalla
, and
R.
Panneton
, “
Evaluation of the acoustic and non-acoustic properties of sound absorbing materials using a three-microphone impedance tube
,”
Appl. Acoust.
71
(
6
),
506
509
(
2010
).
19.
R.
Panneton
and
X.
Olny
, “
Acoustical determination of the parameters governing viscous dissipation in porous media
,”
J. Acoust. Soc. Am.
119
(
4
),
2027
2040
(
2006
).
20.
X.
Olny
and
R.
Panneton
, “
Acoustical determination of the parameters governing thermal dissipation in porous media
,”
J. Acoust. Soc. Am.
123
(
2
),
814
824
(
2008
).
21.
H.-S.
Tsay
and
F.-H.
Yeh
, “
Analysis of mode shapes of a rigidly backed cylindrical foam using three-dimensional finite element acoustical analysis
,”
Appl. Acoust.
69
(
9
),
778
788
(
2008
).
22.
T. E.
Vigran
,
L.
Kelders
,
W.
Lauriks
,
P.
Leclaire
, and
T. F.
Johansen
, “
Prediction and measurements of the influence of boundary conditions in a standing wave tube
,”
Acta Acust. Acust.
83
,
419
423
(
1997
).
23.
B. H.
Song
and
J. S.
Bolton
, “
Investigation of the vibrational modes of edge-constrained fibrous samples placed in a standing wave tube
,”
J. Acoust. Soc. Am.
113
(
4
),
1833
1849
(
2003
).
24.
K. V.
Horoshenkov
,
A.
,
Khan
,
F.-X.
Becot
,
L.
Jaouen
,
F.
Sgard
,
A.
Renault
,
N.
Amirouche
,
F.
Pompoli
,
N.
Prodi
,
P.
Bonfiglio
,
G.
Pispola
,
F.
Asdrubali
,
J.
Hubelt
,
N.
Atalla
,
C. K.
Amedin
,
W.
Lauriks
, and
L.
Boeckx
, “
Reproducibility experiments on measuring acoustical properties of rigid-frame porous media (round-robin tests)
,”
J. Acoust. Soc. Am.
122
(
1
),
345
353
(
2007
).
25.
S. M.
Hasheminejad
and
M. A.
Alibakhshi
, “
Diffraction of sound by a poroelastic cylindrical absorber near an impedance plane
,”
Int. J. Mech. Sci.
49
(
1
),
1
12
(
2007
).
26.
Y.
Zhou
,
Y.
Wang
,
L.
Ma
, and
T.
Gao
, “
Sound scattering by fluid-saturated porous cylinders
,”
Acta Phys. Sin.
49
(
3
),
480
486
(
2000
).
27.
Y.
Liu
, “
Scattering of elastic wave by an absorbing cylinder
,”
Acta Automatica Sin.
24
(
6
),
481
489
(
1998
).
28.
J.
Laperre
and
W.
Thys
, “
Scattering of ultrasonic waves by an immersed porous cylinder
,”
Acoust. Lett.
16
(
1
),
9
(
1992
).
29.
E.
Ogam
,
C.
Depollier
, and
Z. E. A.
Fellah
, “
The direct and inverse problems of an air-saturated porous cylinder submitted to acoustic radiation
,”
Rev. Sci. Instrum.
81
(
9
),
094902
(
2010
).
30.
J.-F.
Allard
and
N.
Atalla
,
Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials
, 2nd ed. (
Wiley
,
West Sussex, UK
,
2009
), Chaps. 5 and 6.
31.
Z. E. A.
Fellah
,
F. G.
Mitri
,
M.
Fellah
,
E.
Ogam
, and
C.
Depollier
, “
Ultrasonic characterization of porous absorbing materials: Inverse problem
,”
J. Sound Vib.
302
(
4–5
),
746
759
(
2007
).
32.
Ph.
Leclaire
,
L.
Kelders
,
W.
Lauriks
,
J. F.
Allard
, and
C.
Glorieux
, “
Ultrasonic wave propagation in reticulated foams saturated by different gases: High frequency limit of the classical models
,”
Appl. Phys. Lett.
69
(
18
),
2641
2643
(
1996
).
33.
M. A.
Biot
, “
Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range
,”
J. Acoust. Soc. Am.
28
(
2
),
168
178
(
1956
).
34.
M. A.
Biot
, “
Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range
,”
J. Acoust. Soc. Am.
28
(
2
),
179
191
(
1956
).
35.
D. L.
Johnson
,
J.
Koplik
, and
R.
Dashen
, “
Theory of dynamic permeability and tortuosity in fluid-saturated porous media
,”
J. Fluid Mech.
176
(
1
),
379
402
(
1987
).
36.
Y.
Champoux
and
J.-F.
Allard
, “
Dynamic tortuosity and bulk modulus in air-saturated porous media
,”
J. Appl. Phys.
70
,
1975
1979
(
1991
).
37.
Y.
Champoux
and
M. R.
Stinson
, “
On acoustical models for sound propagation in rigid frame porous materials and the influence of shape factors
,”
J. Acoust. Soc. Am.
92
(
2
),
1120
1131
(
1992
).
38.
D.
Lafarge
,
P.
Lemarinier
,
J.-F.
Allard
, and
V.
Tarnow
, “
Dynamic compressibility of air in porous structures at audible frequencies
,”
J. Acoust. Soc. Am.
102
(
4
),
1995
2006
(
1997
).
39.
J.-F.
Allard
and
Y.
Champoux
, “
New empirical equations for sound propagation in rigid frame fibrous materials
,”
J. Acoust. Soc. Am.
91
(
6
),
3346
3353
(
1992
).
40.
M.
Sadouki
,
M.
Fellah
,
Z. E. A.
Fellah
,
E.
Ogam
,
N.
Sebaa
,
F. G.
Mitri
, and
C.
Depollier
, “
Measuring static thermal permeability and inertial factor of rigid porous materials
,”
J. Acoust. Soc. Am.
130
(
5
),
2627
2630
(
2011
).
41.
Z. E. A.
Fellah
,
M.
Fellah
,
F. G.
Mitri
,
N.
Sebaa
,
W.
Lauriks
, and
C.
Depollier
, “
Transient acoustic wave propagation in air-saturated porous media at low frequencies
,”
J. Appl. Phys.
102
(
8
),
084906
(
2007
).
42.
M.
Abramowitz
and
I. A.
Stegun
,
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
(
Dover
,
New York
,
1964
), Chap. 9.
43.
J. A.
Kong
,
Electromagnetic Wave Theory
(
Electromagnetic wave Publishing
,
Cambridge, MA
,
2008
), Chap. 7.2, pp.
782
783
.
44.
P. M.
Morse
and
K. U.
Ingard
,
Theoretical Acoustics
(
McGraw-Hill
,
New York
,
1968
), Chap. 8.
45.
K. O.
Geddes
,
G.
Labahn
, and
M.
Monagan
,
Maple 12 Advanced Programming Guide
(
Computer Science Department, University of Waterloo
,
Ontario, Canada
,
2010
).
46.
L. J.
Gibson
and
M. F.
Ashby
,
Cellular Solids: Structure and Properties
, 2nd ed. (
Cambridge Solid State Science, Cambridge University Press
,
1997
).
47.
D. T.
DiPerna
and
T. K.
Stanton
, “
Fresnel zone effects in the scattering of sound by cylinders of various lengths
,”
J. Acoust. Soc. Am.
90
(
6
),
3348
3355
(
1991
).
48.
Agilent
,
Agilent, E.2094S IO Libraries Suite 15.5
(
Agilent Technologies, Inc.
,
Santa Clara, CA
,
2009
), Data Sheet 5989-1439EN.
49.
L.
Jaouen
,
A.
Renault
, and
M.
Deverge
, “
Elastic and damping characterizations of acoustical porous materials: Available experimental methods and applications to a melamine foam
,”
Appl. Acoust.
69
(
12
),
1129
1140
(
2008
).
50.
L.
Boeckx
,
P.
Leclaire
,
P.
Khurana
,
C.
Glorieux
,
W.
Lauriks
, and
J. F.
Allard
, “
Investigation of the phase velocities of guided acoustic waves in soft porous layers
,”
J. Acoust. Soc. Am.
117
(
2
),
545
554
(
2005
).
51.
N.
Geebelen
,
L.
Boeckx
,
G.
Vermeir
,
W.
Lauriks
,
J. F.
Allard
, and
O.
Dazel
, “
Measurement of the rigidity coefficients of a melamine foam
,”
Acta Acust. Acust.
93
,
783
788
(
2007
).
52.
R.
Dragonetti
,
C.
Ianniello
, and
R. A.
Romano
, “
Measurement of the resistivity of porous materials with an alternating air-flow method
,”
J. Acoust. Soc. Am.
129
(
2
),
753
764
(
2011
).
53.
J. D.
Kaplunov
and
D. G.
Markushevich
, “
Plane vibrations and radiation of an elastic layer lying on a liquid half-space
,”
Wave Motion
17
(
3
),
199
211
(
1993
).
54.
J. D.
Achenbach
,
Wave Propagation in Elastic Solids
(
North-Holland
,
New York
,
1973
), pp.
1
426
.
55.
E.
Ogam
, “
Recovery of airflow resistivity of poroelastic beams submitted to transient mechanical stress
,”
Mech. Syst. Signal Process.
34
(
1–2
),
393
407
(
2013
).
56.
C.
Perrot
,
F.
Chevillotte
, and
R.
Panneton
, “
Bottom-up approach for microstructure optimization of sound absorbing materials
,”
J. Acoust. Soc. Am.
124
(
2
),
940
948
(
2008
).
57.
A.
Moussatov
,
C.
Ayrault
, and
B.
Castagnède
, “
Porous material characterization-ultrasonic method for estimation of tortuosity and characteristic length using a barometric chamber
,”
Ultrasonics
39
(
3
),
195
202
(
2001
).
58.
Z. E. A.
Fellah
,
M.
Fellah
,
F. G.
Mitri
,
N.
Sebaa
,
C.
Depollier
, and
W.
Lauriks
, “
Measuring permeability of porous materials at low frequency range via acoustic transmitted waves
,”
Rev. Sci. Instrum.
78
(
11
),
114902
(
2007
).
59.
L.
Jaouen
,
B.
Brouard
,
N.
Atalla
, and
C.
Langlois
, “
A simplified numerical model for a plate backed by a thin foam layer in the low frequency range
,”
J. Sound Vib.
280
(
3–5
),
681
698
(
2005
).
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