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

Cherednichenko, K.D.; Cooper, S.

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.

Citation

Cherednichenko, K., & Cooper, S. (2015). On the existence of high-frequency boundary resonances in layered elastic media. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2178), Article 20140878. https://doi.org/10.1098/rspa.2014.0878

• Journal Article Type: Article
• Acceptance Date: Apr 1, 2015
• Online Publication Date: May 13, 2015
• Publication Date: Jun 8, 2015
• Deposit Date: Oct 31, 2017
• Publicly Available Date: Apr 23, 2018
• Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-5021
• Electronic ISSN: 1471-2946
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 471
• Issue: 2178
• Article Number: 20140878
• DOI: https://doi.org/10.1098/rspa.2014.0878
• Public URL: https://durham-repository.worktribe.com/output/1341459