Skip to main content

Research Repository

Advanced Search

An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces.

Wootton, P.T.; Kaplunov, J.; Colquitt, D.J.

An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces. Thumbnail


Authors

P.T. Wootton

D.J. Colquitt



Abstract

We consider a periodic array of resonators, formed from Euler-Bernoulli beams, attached to the surface of an elastic half-space. Earlier studies of such systems have concentrated on compressional resonators. In this paper, we consider the effect of the flexural motion of the resonators, adapting a recently established asymptotic methodology that leads to an explicit scalar hyperbolic equation governing the propagation of Rayleigh-like waves. Compared with classical approaches, the asymptotic model yields a significantly simpler dispersion relation, with closed-form solutions, shown to be accurate for surface wave-speeds close to that of the Rayleigh wave. Special attention is devoted to the effect of various junction conditions joining the beams to the elastic half-space which arise from considering flexural motion and are not present for the case of purely compressional resonators. Such effects are shown to provide significant and interesting features and, in particular, the choice of junction conditions dramatically changes the distribution and sizes of stop bands. Given that flexural vibrations in thin beams are excited more readily than compressional modes and the ability to model elastic surface waves using the scalar wave equation (i.e. waves on a membrane), the paper provides new pathways towards novel experimental set-ups for elastic metasurfaces.

Journal Article Type Article
Acceptance Date Jun 17, 2019
Online Publication Date Jul 24, 2019
Publication Date Jul 26, 2019
Publicly Available Date Mar 29, 2024
Journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-5021
Publisher The Royal Society
Peer Reviewed Peer Reviewed
Volume 475
Issue 2227
DOI https://doi.org/10.1098/rspa.2019.0079
Keywords surface waves, resonant arrays, asymptotic, Rayleigh waves
Publisher URL https://royalsocietypublishing.org/doi/10.1098/rspa.2019.0079

Files




You might also like



Downloadable Citations