Platonic Localisation: One Ring to Bind Them



Movchan, AB, McPhedran, RC, Carta, G ORCID: 0000-0003-1325-8070 and Craster, RV
(2019) Platonic Localisation: One Ring to Bind Them. Archive of Applied Mechanics, 89 (3). 521 - 533.

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Abstract

In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring-mass resonators in an elastic plate. The values for the required masses and stiffnesses of resonators are derived in a closed analytical form. It is shown that spring-mass resonators can be tuned to produce a "negative inertia" input, which is used to enhance localisation of waveforms around the structured ring. Theoretical findings are accompanied by numerical simulations, which show exponentially localised and leaky modes for different frequency regimes.

Item Type: Article
Additional Information: 15 pages, 9 figures
Uncontrolled Keywords: Flexural waves, Localisation, Asymptomatics, Homogenisation
Depositing User: Symplectic Admin
Date Deposited: 15 Jan 2019 11:09
Last Modified: 10 Jun 2021 23:12
DOI: 10.1007/s00419-018-1465-8
Open Access URL: https://link.springer.com/content/pdf/10.1007/s004...
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3031051