Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction

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Title: Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction
Authors: Colquitt, DJ
Colombi, A
Craster, RV
Roux, P
Guenneau, SRL
Item Type: Journal Article
Abstract: We consider the canonical problem of an array of rods, which act as resonators, placed on an elastic substrate; the substrate being either a thin elastic plate or an elastic half-space. In both cases the flexural plate, or Rayleigh surface, waves in the substrate interact with the resonators to create interesting effects such as effective band-gaps for surface waves or filters that transform surface waves into bulk waves; these effects have parallels in the field of optics where such sub-wavelength resonators create metamaterials, and metasurfaces, in the bulk and at the surface respectively. Here we carefully analyse this canonical problem by extracting the dispersion relations analytically thereby examining the influence of both the flexural and compressional resonances on the propagating wave. For an array of resonators atop an elastic half-space we augment the analysis with numerical simulations. Amongst other effects, we demonstrate the striking effect of a dispersion curve that transitions from Rayleigh wave-like to shear wave-like behaviour and the resultant change in displacement from surface to bulk waves.
Issue Date: 8-Dec-2016
Date of Acceptance: 4-Dec-2016
ISSN: 0022-5096
Publisher: Elsevier
Start Page: 379
End Page: 393
Journal / Book Title: Journal of the Mechanics and Physics of Solids
Volume: 99
Copyright Statement: © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/I019111/1
Keywords: Science & Technology
Physical Sciences
Materials Science, Multidisciplinary
Physics, Condensed Matter
Materials Science
Elastic surface waves
Floquet-Bloch theory
Effective band gaps
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Mechanical Engineering & Transports
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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