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

Kirill Cherednichenko; Shane Cooper

doi:10.1098/rspa.2014.0878

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

Kirill Cherednichenko, Shane Cooper

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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.

Original language	English
Pages (from-to)	1 - 16
Number of pages	16
Journal	Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Volume	471
Issue number	2178
Early online date	8 Jun 2015
DOIs	https://doi.org/10.1098/rspa.2014.0878
Publication status	Published - 8 Jun 2015

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10.1098/rspa.2014.0878Licence: CC BY

IAA - New-wave Damping Composites
Cherednichenko, K. (PI), Blondel, P. (CoI) & Cooper, S. (CoI)
Engineering and Physical Sciences Research Council
5/09/16 → 28/02/17
Project: Research council

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IAA - 1st International Workshop on the Application of Nanolime for Stone Consolidation
Ball, R. (PI)
Engineering and Physical Sciences Research Council
1/03/15 → 30/09/15
Project: Research council
Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Cherednichenko, K. (PI)
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council

Cite this

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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.",

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AU - Cooper, Shane

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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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DO - 10.1098/rspa.2014.0878

M3 - Article

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VL - 471

SP - 1

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JO - Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences

IS - 2178

ER -

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

Abstract

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Projects

IAA - New-wave Damping Composites

IAA - 1st International Workshop on the Application of Nanolime for Stone Consolidation

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this