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Un problème Spectral Issu d'un Couplage Elasto-Acoustique

Published online by Cambridge University Press:  15 April 2002

Mario Durán  and
Jean-Claude Nédélec
Mario Durán
Affiliation:
Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile. (mduran@mat.puc.cl)
Jean-Claude Nédélec
Affiliation:
Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France. (nedelec@cmap.polytechnique.fr)
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Abstract

We are interested in the theoretical study of a spectral problem arising in a physical situation, namely interactions of fluid-solid type structure. More precisely, we study the existence of solutions for a quadratic eigenvalue problem, which describes the vibrations of a system made up of two elastic bodies, where a slip is allowed on their interface and which surround a cavity full of an inviscid and slightly compressible fluid. The problem shall be treated like a generalized eigenvalue problem. Thus by using some functional analysis results, we deduce the existence of solutions and prove a spectral asymptotic behavior property, which allows us to compare the spectrum of this coupled model and the spectrum associated to the problem without transmission between the fluid-solid media.

Keywords

Couplage élasto-acoustiqueproblème quadratique de valeurs propres.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 4 , July 2000 , pp. 835 - 857
Copyright
© EDP Sciences, SMAI, 2000

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References

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