Abstract
The paper presents a systematic study of dispersive waves in an elastic chiral lattice. Chirality is introduced through gyroscopes embedded into the junctions of a doubly periodic lattice. Bloch–Floquet waves are assumed to satisfy the quasi-periodicity conditions on the elementary cell. New features of the system include degeneracy due to the rotational action of the built-in gyroscopes and polarisation leading to the dominance of shear waves within a certain range of values of the constant characterising the rotational action of the gyroscopes. Special attention is given to the analysis of Bloch–Floquet waves in the neighbourhoods of critical points of the dispersion surfaces, where standing waves of different types occur. The theoretical model is accompanied by numerical simulations demonstrating directional localisation and dynamic anisotropy of the system.
Highlights
Propagation of waves in periodic discrete media has received increasing attention in recent years, the first studies date back several decades (Brillouin, 1953; Kittel, 1956)
This work has demonstrated the effects of a system of gyroscopes on the dynamic properties of a monatomic lattice
The analytical findings concerning the dispersive properties of the medium have been confirmed by the illustrative numerical simulations
Summary
Propagation of waves in periodic discrete media has received increasing attention in recent years, the first studies date back several decades (Brillouin, 1953; Kittel, 1956). The study by Brun et al (2012) introduced monatomic and biatomic lattice systems with embedded gyros This was a novel idea leading to unusual degeneracies and a coupling mechanism between shear and pressure waves. It remained a challenge to model forced lattice systems with built-in gyros in the high frequency regime This challenge is addressed in the present paper to the extent that the critical points have been fully classified and the important effects of dynamic anisotropy have been studied. These computations focus, in particular, on illustrations of properties of the dynamic response of the system for frequencies chosen in the neighbourhoods of critical points of the dispersion surfaces. Special attention is given to directional preference and localisation induced by the rotational action of the gyros embedded in the lattice
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