Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer

Victor Péron

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 5, page 1431-1449
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Péron, Victor. "Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.5 (2014): 1431-1449. <http://eudml.org/doc/273232>.

@article{Péron2014,
abstract = {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.},
author = {Péron, Victor},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {asymptotic expansions; equivalent boundary conditions; elasto-acoustic coupling; diffraction problem; transmission problem},
language = {eng},
number = {5},
pages = {1431-1449},
publisher = {EDP-Sciences},
title = {Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer},
url = {http://eudml.org/doc/273232},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Péron, Victor
TI - Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 5
SP - 1431
EP - 1449
AB - 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.
LA - eng
KW - asymptotic expansions; equivalent boundary conditions; elasto-acoustic coupling; diffraction problem; transmission problem
UR - http://eudml.org/doc/273232
ER -

References

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