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Equivalent Boundary Conditions for an Elasto-Acoustic Problemset in a Domain with a Thin Layer∗

Published online by Cambridge University Press:  13 August 2014

Victor Péron
Victor Péron*
Affiliation:
LMAP CNRS UMR 5142 & Team MAGIQUE 3D INRIA Bordeaux Sud-Ouest, Université de Pau et des Pays de l’Adour, Avenue de l’Université, BP 1155, 64013 Pau Cedex, France.. victor.peron@univ-pau.fr
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Abstract

We present equivalent conditions and asymptotic models for the diffraction problem ofelastic and acoustic waves in a solid medium surrounded by a thin layer of fluid medium.Due to the thinness of the layer with respect to the wavelength, this problem is wellsuited for the notion of equivalent conditions and the effect of the fluid medium on thesolid is as a first approximation local. We derive and validate equivalent conditions upto the fourth order for the elastic displacement. These conditions approximate theacoustic waves which propagate in the fluid region. This approach leads to solve onlyelastic equations. The construction of equivalent conditions is based on a multiscaleexpansion in power series of the thickness of the layer for the solution of thetransmission problem.

Keywords

Asymptotic expansionsequivalent boundary conditionselasto-acoustic coupling
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 5 , September 2014 , pp. 1431 - 1449
Copyright
© EDP Sciences, SMAI 2014

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