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.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Reference18 articles.
1. RAYLEIGH WAVES ON ELASTIC CRYSTALS
2. Foundations of the theory of surface waves in anisotropic elastic materials;Chadwick P;Adv. Appl. Mech.,1973
3. Lecture Notes in Physics, no. 127;Palencia ES,1980
4. Homogenization and Two-Scale Convergence
5. On an extension of the method of two-scale convergence and its applications
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