This paper provides a temporal model of the direct scattering problem for the propagation of transient low frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. In this model, the inertial effects are described by the low frequency approximation of the tortuosity. The viscous and thermal losses of the medium are modeled by viscous and thermal permeabilities. The propagation equation is derived and solved analytically in the time domain. An original expression of Green’s function of the porous medium is obtained. The transmission scattering operator of the first transmitted wave is calculated and compared with experimental data.

1.
J. F.
Allard
,
Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials
(
Chapman and Hall
,
London
,
1993
).
2.
G.
Caviglia
and
A.
Morro
,
J. Acoust. Soc. Am.
116
,
643
(
2004
).
3.
G. V.
Norton
and
J. C.
Novarini
,
J. Acoust. Soc. Am.
113
,
3024
(
2003
).
4.
W.
Chen
and
S.
Holm
,
J. Acoust. Soc. Am.
113
,
3024
(
2003
).
5.
Z. E. A.
Fellah
,
M.
Fellah
,
W.
Lauriks
, and
C.
Depollier
,
J. Acoust. Soc. Am.
113
,
61
(
2003
).
6.
Z. E. A.
Fellah
,
C.
Depollier
,
S.
Berger
,
W.
Lauriks
,
P.
Trompette
, and
J. Y.
Chapelon
,
J. Acoust. Soc. Am.
114
,
2561
(
2003
).
7.
Z. E. A.
Fellah
,
F. G.
Mitri
,
C.
Depollier
,
S.
Berger
,
W.
Lauriks
, and
J. Y.
Chapelon
,
J. Appl. Phys.
94
,
7914
(
2003
).
8.
Z. E. A.
Fellah
,
S.
Berger
,
W.
Lauriks
, and
C.
Depoller
,
J. Sound Vib.
270
,
865
(
2004
).
9.
T. L.
Szabo
,
J. Acoust. Soc. Am.
96
,
491
(
1994
).
10.
T. L.
Szabo
,
J. Acoust. Soc. Am.
97
,
14
(
1995
).
11.
Z. E. A.
Fellah
and
C.
Depollier
,
J. Acoust. Soc. Am.
107
,
683
(
2000
).
12.
Z. E. A.
Fellah
,
M.
Fellah
,
N.
Sebaa
,
W.
Lauriks
, and
C.
Depollier
,
J. Acoust. Soc. Am.
119
,
1926
(
2006
).
13.
M. E.
Delany
and
E. N.
Bazley
,
Appl. Acoust.
3
,
105
(
1970
).
14.
D. A.
Bies
and
C. H.
Hansen
,
Appl. Acoust.
13
,
357
(
1980
).
15.
D.
Lafarge
, “
Sound propagation in porous materials having a rigid frame saturated by gas
.” Ph.D. dissertation,
Université du Maine
,
1993
.
16.
D.
Lafarge
,
P.
Lamarnier
,
J. F.
Allard
, and
V.
Tarnow
,
J. Acoust. Soc. Am.
102
,
1995
(
1996
).
17.
L. L.
Beranek
,
J. Acoust. Soc. Am.
13
,
248
(
1942
).
18.
M. A.
Biot
,
J. Acoust. Soc. Am.
28
,
168
(
1956
).
19.
M. A.
Biot
,
J. Acoust. Soc. Am.
28
,
179
(
1956
).
20.
A. N.
Norris
,
J. Wave-Mater. Interact.
1
,
365
(
1986
).
21.
D. L.
Johnson
,
J.
Koplik
, and
R.
Dashen
,
J. Fluid Mech.
176
,
379
(
1987
).
22.
I. S.
Gradshteyn
and
I. M.
Ryzhik
,
Table of Integrals, Series and Products
, 4th ed. (
Academic
,
New York
,
1965
).
You do not currently have access to this content.