Low-frequency wave-energy amplification in graded two-dimensional resonator arrays
File(s)
Accepted version
Author(s)
Bennetts, LG
Peter, MA
Craster, RV
Type
Journal Article
Abstract
Energy amplification in square-lattice arrays of C-shaped low-frequency resonators, where the resonator radii are graded with distance, is investigated in the two-dimensional linear acoustics setting for both infinite (in one dimension) and finite arrays. Large amplifications of the incident energy are shown in certain array locations. The phenomenon is analysed using: (i) band diagrams for doubly-periodic arrays; (ii) numerical simulations for infinite and finite arrays; and (iii) eigenvalue analysis of transfer matrices operating over individual columns of the array. It is shown that the locations of the large amplifications are predicted by propagation cut-offs in the modes associated with the transfer-matrix eigenvalues. For the infinite array, the eigenvalues form a countable set, and for the low frequencies considered, only a single propagating mode exists for a given incident wave, which cuts off within the array, leading to predictive capabilities for the amplification location. For the finite array, it is shown that (in addition to a continuous spectrum of modes) multiple discrete propagating modes can be excited, with the grading generating new modes, as well as cutting others off, leading to complicated amplification patterns. The numerical simulations reveal that the largest amplifications are achieved for a single row array, with amplifications an order of magnitude smaller for the corresponding infinite array.
Date Issued
2019-10-21
Date Acceptance
2019-06-27
Citation
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019, 377 (2156)
ISSN
1364-503X
Publisher
The Royal Society
Journal / Book Title
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
377
Issue
2156
Copyright Statement
© 2019 The Author(s). Published by the Royal Society. All rights reserved.
Sponsor
UKRI
Engineering & Physical Science Research Council (E
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000484036800006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/T002654/1
R100724-101, A/C 86440
EP/L024926/1
Subjects
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
rainbow trapping
wave scattering
graded diffraction gratings
SCATTERING
SPECTRA
ROWS
Publication Status
Published
Article Number
ARTN 20190104
Date Publish Online
2019-09-02