An acoustic model is developed for transient wave propagation in a weak layer excited by prescribed pressure or prescribed acceleration at the boundary. The validity of the acoustic model is investigated for the two excitations. A comparison of transient response from the acoustic model and a 3D axisymmetric elastic model reveals that for prescribed acceleration the acoustic model fails to capture important features of the elastic model even as Poisson ratio ν approaches 12. However for prescribed pressure, the two models agree since shear stress is reduced. For prescribed acceleration adopting the modal approach, the mixed boundary-value problem on the excited boundary is converted to a pure traction problem utilizing the influence method. To validate the elaborate modal approach a finite difference model is also developed.

1.
Theil
,
F.
, 1998, “
Young-Measure Solutions for a Viscoelastically Damped Wave Equation with Nonmonotone Stress-Strain Relation
,”
Arch. Ration. Mech. Anal.
0003-9527,
144
, pp.
47
78
.
2.
Yserentant
,
H.
, 2001, “
The Propagation of Sound in Particle Models of Compressible Fluids
,”
Numer. Math.
0029-599X,
88
, pp.
581
601
.
3.
Yserentant
,
H.
, 1997, “
A Particle Model of Compressible Fluids
,”
Numer. Math.
0029-599X,
76
, pp.
111
142
.
4.
Sina
,
K.
, and
Khashayar
,
M.
, 2002, “
Analytical Solution of Wave Equation for Arbitrary Non-Homogeneous Media
,”
Proceedings of SPI, The International Society of Optical Engineering 4772
, pp.
25
36
.
5.
Sujith
,
R.
,
Bala Subrahmanyam
,
P. T.
, and
Lieuwen
,
P.
, 2003, “
Propagation of Sound in Inhomogeneous Media: Exact Solutions in Curvilinear Geometries
,”
ASME J. Vibr. Acoust.
0739-3717,
125
, pp.
133
136
.
6.
Hamdi
,
S.
,
Enright
,
W.
,
Schiesser
,
W.
, and
Gottlieb
,
J.
, 2003, “
Exact Solutions of the Generalized Equal Width Wave Equation
,”
Lect. Notes Comput. Sci.
0302-9743,
266
, pp.
725
734
.
7.
Yang
,
D.
, 1994, “
Grid Modification for the Wave Equation with Attenuation
,”
Numer. Math.
0029-599X,
67
, pp.
391
401
.
8.
Narayan
,
J.
, 1998, “
2.5-D Numerical Simulation of Acoustic Wave Propagation
,”
Pure Appl. Geophys.
0033-4553,
151
, pp.
47
61
.
9.
Schemann
,
M.
, and
Bornemann
,
F.
, 1998, “
An Adaptive Rothe Method for the Wave Equation
,”
Computing and Visualization in Science
,
3
, pp.
137
144
.
10.
Bailly
,
C.
, and
Juve
,
D.
, 2000, “
Numerical solution of acoustic propagation problems using linearized Euler equations
,”
AIAA J.
0001-1452,
38
, pp.
22
29
.
11.
Wagner
,
G.
,
Wenzel
,
M.
, and
Dumont
,
W.
, 2001, “
Numerical treatment of acoustic problems with the hybrid boundary element method
,”
Int. J. Solids Struct.
0020-7683,
38
, pp.
10
13
;
Wagner
,
G.
,
Wenzel
,
M.
, and
Dumont
,
W.
,
Int. J. Solids Struct.
0020-7683,
38
, pp.
1871
1888
.
12.
Gaul
,
L.
, and
Wenzel
,
M.
, 2001, “
Acoustic calculations with the hybrid boundary element method in the time domain
,”
Eng. Anal. Boundary Elem.
0955-7997,
25
, pp.
259
265
.
13.
Mehdizadeh
,
O.
, and
Paraschivoiu
,
M.
, 2003, “
Investigation of a Three-Dimensional Spectral Element Method for Helmholtz’s Equation
,”
Lect. Notes Comput. Sci.
0302-9743,
2668
, pp.
819
825
.
14.
Berry
,
J.
, and
Naghdi
,
P.
, 1956, “
On the Vibration of Elastic Bodies Having Time Dependent Boundary Conditions
,”
Q. Appl. Math.
0033-569X,
14
, pp.
43
50
.
15.
El-Raheb
,
M.
, 2004, “
Wave Propagation in a Weak Viscoelastic Layer Produced by Prescribed Velocity on the Boundary
,”
J. Sound Vib.
0022-460X,
275
(
1–2
), pp.
89
106
.
16.
Eisler
,
R.
, 2003, (
private communication
, Mission Research Corporation, Laguna Hills, CA).
17.
Landau
,
L.
, and
Lifshitz
,
E.
, 1959,
Fluid Mechanics
,
1st English Ed.
,
Pergamon Press
, Addison-Wesley, New York.
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