Analysis of three-dimensional sound propagation in porous elastic media with the Finite Element (FE) method is, in general, computationally costly. Although it is the most commonly used predictive tool in complex noise control applications, efficient FE solution strategies for large-size industrial problems are still lacking. In this work, an original procedure is proposed for the sorting and selection of the modes in the solution for the sound field in homogeneous porous domains. This procedure, validated on several 2D and 3D problems, enables to reduce the modal basis in the porous medium to its most physically significant components. It is shown that the size of the numerical problem can be reduced, together with matrix sparsity improvements, which lead to the reduction in computational time and enhancements in the efficacy of the acoustic response computation. The potential of this method for other industrial-based noise control problems is also discussed.

1.
M. A.
Biot
, “
Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range
,”
J. Acoust. Soc. Am.
28
,
168
178
(
1956
).
2.
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
).
3.
M. A.
Biot
, “
Generalized theory of acoustic propagation in porous dissipative media
,”
J. Acoust. Soc. Am.
34
(
9
),
1254
1264
(
1962
).
4.
J.-F.
Allard
and
N.
Atalla
,
Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials
(
Wiley
,
New York
,
2009
),
372
pp.
5.
N.
Atalla
,
M. A.
Hamdi
, and
R.
Panneton
, “
Enhanced weak integral formulation for the mixed (u,p) poroelastic equations
,”
J. Acoust. Soc. Am.
109
(
6
),
3065
3068
(
2001
).
6.
Y. J.
Kang
and
J. S.
Bolton
, “
Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements
,”
J. Acoust. Soc. Am.
98
,
635
643
(
1995
).
7.
O.
Dazel
,
F.
Sgard
, and
C.-H.
Lamarque
, “
Application of generalized complex modes to the calculation of the forced response of three-dimensional poroelastic materials
,”
J. Sound Vib.
268
(
3
),
555
580
(
2003
).
8.
P.
Davidsson
and
G.
Sandberg
, “
A reduction method for structure-acoustic and poroelastic-acoustic problems using interface-dependent lanczos vectors
,”
Comput. Methods Appl. Mech. Eng.
195
(
17–18
),
1933
1945
(
2006
).
9.
C.
Batifol
,
M. N.
Ichchou
, and
M. A.
Galland
, “
Hybrid modal reduction for poroelastic materials
,”
C. R. Mécan.
336
(
10
),
757
765
(
2008
).
10.
O.
Dazel
,
B.
Brouard
,
N.
Dauchez
, and
A.
Geslain
, “
Enhanced Biot's finite element displacement formulation for porous materials and original resolution methods based on normal modes
,”
Acta Acust. Acust.
95
(
3
),
527
538
(
2009
).
11.
O.
Dazel
,
B.
Brouard
,
N.
Dauchez
,
A.
Geslain
, and
C. H.
Lamarque
, “
A free interface CMS technique to the resolution of coupled problem involving porous materials, application to a monodimensional problem
,”
Acta Acust. Acust.
96
(
2
),
247
257
(
2010
).
12.
R.
Rumpler
,
J.-F.
Deü
, and
P.
Göransson
, “
A modal-based reduction method for sound absorbing porous materials in poro-acoustic finite element models
,”
J. Acoust. Soc. Am.
132
(
5
),
3162
3179
(
2012
).
13.
R.
Rumpler
, “
Efficient finite element approach for structural-acoustic applications including 3D modelling of sound absorbing porous materials
,” PhD Thesis (
Cnam/KTH, Paris/Stockholm
,
2012
),
205
pp.
14.
R.
Rumpler
,
A.
Legay
, and
J.-F.
Deü
, “
Performance of a restrained-interface substructuring FE model for reduction of structural-acoustic problems with poroelastic damping
,”
Comput. Struct.
89
(
23–24
),
2233
2248
(
2011
).
15.
G.
Kergourlay
,
E.
Balmes
, and
D.
Clouteau
, “
Model reduction for efficient FEM/BEM coupling
,”
Proc. Int. Sem. Modal Anal.
3
,
1167
1174
(
2001
).
16.
E.
Balmes
, “
Modes and regular shapes. How to extend component mode synthesis theory
,” in
Proceedings of the XI DINAME-Ouro Preto-MG-Brazil
,
2005
,
14
pp.
17.
E.
Balmes
,
M.
Corus
, and
S.
Germes
, “
Model validation for heavily damped structures. application to a windshield joint
,” in
Proceedings of ISMA 2006
,
2006
, paper 106.
18.
Q. H.
Tran
,
M.
Ouisse
, and
N.
Bouhaddi
, “
A robust component mode synthesis method for stochastic damped vibroacoustics
,”
Mech. Syst. Signal Processing
24
(
1
),
164
181
(
2010
).
19.
A.
Bouazzouni
,
G.
Lallement
, and
S.
Cogan
, “
Selecting a ritz basis for the reanalysis of the frequency response functions of modified structures
,”
J. Sound Vib.
199
(
2
),
309
322
(
1997
).
20.
N.
Dauchez
,
S.
Sahraoui
, and
N.
Atalla
, “
Convergence of poroelastic finite elements based on Biot displacement formulation
,”
J. Acoust. Soc. Am.
109
,
33
40
(
2001
).
21.
E.
Balmes
, “
Use of generalized interface degrees of freedom in component mode synthesis
,” In
Proceedings of IMAC
(
1996
), pp.
204
210
.
22.
J.
Herrmann
,
M.
Maess
, and
L.
Gaul
, “
Substructuring including interface reduction for the efficient vibro-acoustic simulation of fluid-filled piping systems
,”
Mech. Syst. Signal Processing
24
(
1
),
153
163
(
2010
).
23.
J. K.
Bennighof
and
R. B.
Lehoucq
, “
An automated multilevel substructuring method for eigenspace computation in linear elastodynamics
,”
SIAM J. Sci. Comput.
25
(
6
),
2084
2106
(
2004
).
24.
E. L.
Wilson
,
M.-W.
Yuan
, and
J. M.
Dickens
, “
Dynamic analysis by direct superposition of Ritz vectors
,”
Earthquake Eng. Struct. Dyn.
10
(
6
),
813
821
(
1982
).
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