Wootton, PT, Kaplunov, J and Colquitt, DJ (2019) An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475 (2227). 20190079 - ?. ISSN 1471-2946

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J Kaplunov - An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces.pdf - Accepted Version
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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.

Item Type: Article
Additional Information: The final version of this accepted manuscript is available from the publisher at https://royalsocietypublishing.org/doi/10.1098/rspa.2019.0079
Uncontrolled Keywords: surface waves, resonant arrays, asymptotic, Rayleigh waves
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Related URLs:
Depositing User: Symplectic
Date Deposited: 10 Sep 2019 10:45
Last Modified: 24 Mar 2021 12:20
URI: https://eprints.keele.ac.uk/id/eprint/6789

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