Comptes Rendus
Hybrid modal reduction for poroelastic materials
Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 757-765.

A modal-like projection method for poroelastic materials is proposed and implemented for finite element calculations. Non-physical Dirichlet conditions are imposed at the junction interface, involving constrained fluid displacements and free solid displacements. The (us,Uf) formulation is used. The resulting frequency-dependent eigenproblem is solved without simplification using the non-linear Arnoldi algorithm. The projection subspace is spanned by calculated dynamic modes and fluid static boundary functions. A convergence study is performed and results are compared to classical Craig and Bampton and MacNeal approaches. The hybrid basis proves to be efficient.

Une méthode de réduction modale pour les matériaux poroélastiques est proposée. Cette procédure de réduction est implémentée lors de calculs éléments finis. Des conditions de Dirichlet non-physiques sont appliquées à l'interface. La phase fluide est ainsi encastrée, contrairement à la phase solide qui est libre. La formulation (us,Uf) est utilisée. Le problème spectral, fréquentiellement dépendant, est résolu sans approximation par l'emploi de l'algorithme d'Arnoldi non-linéaire. Le sous-espace de projection est généré par les modes dynamiques calculés et le relèvement statique fluide. Une étude de convergence est menée, et les résultats sont comparés aux approches classiques de type Craig et Bampton et MacNeal. La base hybride apparaît efficace.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2008.09.005
Keywords: Poroelastic materials, Dynamic substructuring, Modal synthesis
Mot clés : Matériaux poroélastiques, Sous-structuration dynamique, Synthèse modale

Cédric Batifol 1, 2; Mohamed N. Ichchou 1; Marie-Annick Galland 2

1 Laboratoire de tribologie et de dynamique des systèmes, CNRS-UMR 5513, École centrale de Lyon, 36, avenue Guy-de-Collongue, 69134 Ecully cedex, France
2 Laboratoire de mécanique des fluides et d'acoustique, CNRS-UMR 5509, École centrale de Lyon, 36, avenue Guy-de-Collongue, 69134 Ecully cedex, France
@article{CRMECA_2008__336_10_757_0,
     author = {C\'edric Batifol and Mohamed N. Ichchou and Marie-Annick Galland},
     title = {Hybrid modal reduction for poroelastic materials},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {757--765},
     publisher = {Elsevier},
     volume = {336},
     number = {10},
     year = {2008},
     doi = {10.1016/j.crme.2008.09.005},
     language = {en},
}
TY  - JOUR
AU  - Cédric Batifol
AU  - Mohamed N. Ichchou
AU  - Marie-Annick Galland
TI  - Hybrid modal reduction for poroelastic materials
JO  - Comptes Rendus. Mécanique
PY  - 2008
SP  - 757
EP  - 765
VL  - 336
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crme.2008.09.005
LA  - en
ID  - CRMECA_2008__336_10_757_0
ER  - 
%0 Journal Article
%A Cédric Batifol
%A Mohamed N. Ichchou
%A Marie-Annick Galland
%T Hybrid modal reduction for poroelastic materials
%J Comptes Rendus. Mécanique
%D 2008
%P 757-765
%V 336
%N 10
%I Elsevier
%R 10.1016/j.crme.2008.09.005
%G en
%F CRMECA_2008__336_10_757_0
Cédric Batifol; Mohamed N. Ichchou; Marie-Annick Galland. Hybrid modal reduction for poroelastic materials. Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 757-765. doi : 10.1016/j.crme.2008.09.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.09.005/

[1] M.A. Biot Theory of propagation of elastic waves in a fluid-saturated porous solid, J. Acoust. Soc. Am., Volume 28 (1956), pp. 168-178

[2] N. Atalla; R. Panneton; P. Debergue A mixed displacement–pressure formulation for poroelastic materials, J. Acoust. Soc. Am., Volume 104 (1998), pp. 1444-1452

[3] L. Jaouen; B. Brouard; N. Atalla; C. Langlois A simplified numerical model for a plate backed by a thin foam layer in the low frequency range, J. Sound Vib., Volume 280 (2005), pp. 681-698

[4] O. Dazel; F. Sgard; C.-H. Lamarque; N. Atalla An extension of complex modes for the resolution of finite-element poroelastic problems, J. Sound Vib., Volume 253 (2002), pp. 421-445

[5] R. Ohayon Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-shloshing problems, Comput. Meth. Appl. Mech. Engrg., Volume 190 (2001), pp. 3009-3019

[6] J.F. Allard Propagation of Sound in Porous Media. Modelling Sound Absorbing Materials, Elsevier Science, 1993

[7] R. Ohayon; R. Sampaio; C. Soize Dynamic substructuring of damped structures using singular value decomposition, J. Appl. Mech., Volume 64 (1997) no. 2, pp. 292-298

[8] H. Voss, An Arnoldi method for non-linear eigenvalue problems, Tech. report, Dept math., TU Hamburd-Harburg, 2003

[9] A. Ruhe Rational Krylov, a practical algorithm for large sparse nonsymmetric matrix pencils, SIAM J. Sci. Comput., Volume 19 (1998), pp. 1535-1551

[10] R.R. Craig; M.C.C. Bampton Coupling of substructures for dynamic analyses, AIAA J., Volume 6 (1968) no. 7, pp. 1313-1319

[11] R.H. MacNeal A hybrid method of component mode synthesis, J. Computers Structures, Volume 1 (1971) no. 4, pp. 581-601

Cited by Sources:

Comments - Policy