Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer∗
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.
Revised: 13 December 2013
We present equivalent conditions and asymptotic models for the diffraction problem of elastic 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 well suited for the notion of equivalent conditions and the effect of the fluid medium on the solid is as a first approximation local. We derive and validate equivalent conditions up to the fourth order for the elastic displacement. These conditions approximate the acoustic waves which propagate in the fluid region. This approach leads to solve only elastic equations. The construction of equivalent conditions is based on a multiscale expansion in power series of the thickness of the layer for the solution of the transmission problem.
Mathematics Subject Classification: 35C20 / 35J25 / 41A60 / 74F10
Key words: Asymptotic expansions / equivalent boundary conditions / elasto-acoustic coupling
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