Elastic wave dispersion and polarization in a chiral elastic metamaterial

Abstract

The study of wave propagation in chiral elastic systems has important potential applications in areas such as controlling vibrations and wave filtering. Although the behaviour of elastic waves in traditional elastic media is well understood, how elastic waves behave in chiral materials is still to be further explored. We present an analytical study of elastic waves in a new continuous chiral elastic material, focusing on (i) the development of the new continuum model based on a class of discrete elastic metamaterials and (ii) the study of dispersion behaviour of elastic waves in this new chiral material. The effective material developed is isotropic and characterized by both elastic moduli and coupling parameters, associated with chirality. The dispersion relation and the corresponding waveforms are studied to evaluate the general behaviour of wave propagation in this new chiral medium. Different from the property of waves in traditional isotropic elastic media, generally no independent longitudinal or transverse waves can be observed in the new chiral medium except for cases at specific frequencies. The analytical findings are accompanied by illustrative numerical examples to show the general property of the dispersion and wave modes.