Wave polarization and dynamic degeneracy in a chiral elastic lattice

Abstract

<jats:p>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.</jats:p>

Frontal waves and transmissions for temporal laminates and imperfect chiral interfaces

“…Recent work on modelling of chiral waves in elastic lattices by Carta et al [20,21] has provided an explanation of the dynamics of discrete gyroscopic systems in the context of dispersion, localization and dynamic degeneracies. The paper by Nieves et al [22] provided mathematical insight into the vibrations of chiral multi-structures and connections between the discrete non-reciprocal systems and their continuous counterparts.…”

A unifying perspective on linear continuum equations prevalent in science. Part II: Canonical forms for time-harmonic equations

“…Smyshlyaev extended this analysis to elastic waves traveling in extremely anisotropic media [117]. Moreover, in considering lattices of gyroscopic spinners (a spinetic material) Carta, Jones, Movchan, and Movchan [21] found the density matrix is not symmetric, but rather Hermitian (and in the presence of losses it would not even be Hermitian).…”

On waves in multi-scale chiral elastic systems

“…In the papers [26][27][28], a triangular elastic lattice has been considered under the assumption that each nodal point of the lattice is nested on the gyroscopic spinner. Although the configuration is similar to Figure 1, in these papers there are no beams or rods connecting the gyros to the base.…”