On the existence of high-frequency boundary resonances in layered elastic media

Author:

Cherednichenko K. D.1,Cooper S.1

Affiliation:

1. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK

Abstract

We analyse the asymptotic behaviour of high-frequency vibrations of a three-dimensional layered elastic medium occupying the domain Ω =(− a , a ) 3 , a >0. We show that in both cases of stress-free and zero-displacement boundary conditions on the boundary of Ω a version of the boundary spectrum, introduced in Allaire and Conca (1998 J. Math. Pures. Appl. 77, 153–208. ( doi:10.1016/S0021-7824(98)80068-8 )), is non-empty and part of it is located below the Bloch spectrum. For zero-displacement boundary conditions, this yields a new type of surface wave, which is absent in the case of a homogeneous medium.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Reference18 articles.

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5. On an extension of the method of two-scale convergence and its applications

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