English

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.

Keywords

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

R2 v1 2026-06-23T02:46:18.011Z