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Wave polarization and dynamic degeneracy in a chiral elastic lattice

Carta, G, Jones, IS, Movchan, NV and Movchan, AB (2019) Wave polarization and dynamic degeneracy in a chiral elastic lattice. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475 (2232). ISSN 1364-5021

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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 polarization 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 characterize 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.

Item Type: Article
Uncontrolled Keywords: 01 Mathematical Sciences, 02 Physical Sciences, 09 Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Divisions: Maritime & Mechanical Engineering
Publisher: Royal Society, The
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Date Deposited: 06 Feb 2020 10:00
Last Modified: 06 Feb 2020 10:15
DOI or Identification number: 10.1098/rspa.2019.0313
URI: http://researchonline.ljmu.ac.uk/id/eprint/12202

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