Wave polarisation and dynamic degeneracy in a chiral elastic lattice

TL;DR

This paper explores the unique wave behaviors in chiral elastic lattices, introducing vortex waveforms and analyzing their impact on wave polarization and degeneracy, with implications for controlling vibrations.

Contribution

It introduces the concept of vortex waveforms and analyzes their role in wave polarization and degeneracy in chiral elastic lattices, advancing understanding of lattice wave dynamics.

Findings

Identification of vortex waveforms as dominant in certain regimes

Analysis of wave polarization and degeneracy in chiral lattices

Numerical simulations supporting analytical results

Abstract

This paper addresses fundamental questions arising in the theory of Bloch-Floquet waves in chiral elastic lattice systems. This area has received a significant attention in the context of "topologically protected" waveforms. Although practical applications of chiral elastic lattices are widely appreciated, especially in problems of controlling low-frequency vibrations, wave polarisation and filtering, the fundamental questions of the relationship of these lattices to classical waveforms associated with longitudinal and shear waves retain a substantial scope for further development. The notion of chirality is introduced into the systematic analysis of dispersive elastic waves in a doubly-periodic lattice. Important quantitative characteristics of the dynamic response of the lattice, such as lattice flux and lattice circulation, are used in the analysis along with the novel concept of "vortex waveforms" that characterise the dynamic response of the chiral system. We note that the continuum concepts of pressure and shear waves do not apply for waves in a lattice, especially in the case when the wavelength is comparable with the size of the elementary cell of the periodic structure. Special critical regimes are highlighted when vortex waveforms become dominant. Analytical findings are accompanied by illustrative numerical simulations.