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

Kirill Cherednichenko, Shane Cooper

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages1 - 16
Number of pages16
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Volume471
Issue number2178
Early online date13 May 2015
DOIs
StatusPublished - Jun 2015

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elastic media
Boundary conditions
boundary conditions
Zero
Surface Waves
Surface waves
surface waves
Vibration
Asymptotic Behavior
vibration
Three-dimensional

Cite this

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AB - 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.

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