Rayleigh-Bloch, topological edge and interface waves for structured elastic plates
File(s)
Accepted version
Author(s)
Chaplain, GJ
Makwana, MP
Craster, R
Type
Journal Article
Abstract
Galvanised by the emergent fields of metamaterials and topological wave physics, there is currently much interest in controlling wave propagation along structured arrays, and interfacial waves between geometrically different crystal arrangements. We model array and interface waves for structured thin elastic plates, so-called platonic crystals, that share many analogies with their electromagnetic and acoustic counterparts, photonic and phononic crystals, and much of what we present carries across to those systems. These crystals support several forms of edge or array-guided modes, that decay perpendicular to their direction of propagation. To rapidly, and accurately, characterise these modes and their decay we develop a spectral Galerkin method, using a Fourier–Hermite basis, to provide highly accurate dispersion diagrams and mode-shapes, that are confirmed with full scattering simulations. We illustrate this approach using Rayleigh Bloch modes, and generalise high frequency homogenisation, along a line array, to extract the envelope wavelength along the array. Rayleigh–Bloch modes along graded arrays of rings of point masses are investigated and novel forms of the rainbow trapping effect and wave hybridisation are demonstrated. Finally, the method is used to investigate the dispersion curves and mode-shapes of interfacial waves created by geometrical differences in adjoining media.
Date Issued
2019-03-01
Date Acceptance
2019-01-16
Citation
Wave Motion, 2019, 86, pp.162-174
ISSN
0165-2125
Publisher
Elsevier
Start Page
162
End Page
174
Journal / Book Title
Wave Motion
Volume
86
Copyright Statement
© 2019 Elsevier B.V. All rights reserved. . This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000460719000013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/L024926/1
RF-2017-017/9
Subjects
Science & Technology
Technology
Physical Sciences
Acoustics
Mechanics
Physics, Multidisciplinary
Physics
Kirchhoff-Love plate theory
Galerkin spectral method
Hermite functions
Rayleigh Bloch modes
Valleytronics
NEGATIVE REFRACTION
OPTIMUM CHOICE
FREE PARAMETER
SURFACE-WAVES
TRAPPED MODES
TRANSMISSION
Publication Status
Published
Date Publish Online
2019-01-21