Platonic Localisation: One Ring to Bind Them
Classical Physics
2019-05-01 v1
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.
Cite
@article{arxiv.1806.11512,
title = {Platonic Localisation: One Ring to Bind Them},
author = {A. B. Movchan and R. C. McPhedran and G. Carta and R. V. Craster},
journal= {arXiv preprint arXiv:1806.11512},
year = {2019}
}
Comments
15 pages, 9 figures