Approximate impedance operator of an infinite thin strip and stabilization in the context of linear micro-dilatation elasticity

Abstract

The aim of this paper is to give asymptotic models for the impedance of an infinite thin strip in the framework of linear elasticity with voids. We start from a two dimensional transmission problem which models the wave propagation between an elastic body with small distributed voids Ω₋ and a thin coating strip Ωδ+ (δ is supposed to be small enough). We show how to model the effect of the thin coating by an impedance boundary condition on the junction of the elastic two bodies. To this end, we use the techniques of abstract differential equations and asymptotic expansion. We prove also an error estimate.