Hybrid modal reduction for poroelastic materials

Cédric Batifol; Mohamed N. Ichchou; Marie-Annick Galland

doi:10.1016/j.crme.2008.09.005

Hybrid modal reduction for poroelastic materials

Presented by: Huy Duong Bui

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

Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 757-765.

Abstract
Résumé

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 ( $u^{s}, U^{f}$ ) 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 ( $u^{s}, U^{f}$ ) 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: 2007-09-12
Accepted: 2008-09-08
Published online: 2008-10-01

DOI: 10.1016/j.crme.2008.09.005

Keywords: Poroelastic materials, Dynamic substructuring, Modal synthesis
Mots-clés : Matériaux poroélastiques, Sous-structuration dynamique, Synthèse modale

Author's affiliations:

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

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     author = {C\'edric Batifol and Mohamed N. Ichchou and Marie-Annick Galland},
     title = {Hybrid modal reduction for poroelastic materials},
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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/

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