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

TL;DR

This paper develops and validates high-order equivalent boundary conditions for elastic-acoustic wave diffraction in a domain with a thin fluid layer, simplifying the problem to elastic equations only.

Contribution

It introduces a multiscale expansion method to derive and validate fourth-order equivalent conditions for elastic displacement in the presence of a thin fluid layer.

Findings

Equivalent conditions up to fourth order are derived.

The approach simplifies the coupled elastic-acoustic problem.

Validation confirms accuracy of the asymptotic models.

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.