Chiral waves in structured elastic systems: dynamics of a meta-waveguide

Abstract

Summary The notion of meta-surfaces is well established for waves interacting with arrays of periodic resonators. Here, an infinite elastic rod, attached to a system of gyroscopic spinners, is considered. This forms a waveguide with unusual dispersion properties and will be referred to as a chiral meta-waveguide. A class of transient and time-harmonic formulations describing waves in elastic chiral meta-waveguides is addressed. Consideration of a chiral elastic chain leads to the governing equations of the homogenised continuous system. Both analytical and numerical solutions are presented. Features observed for chiral waveforms show resemblance with formulations of quantum physics rather than linear elasticity. For an elementary example related to an elastic chiral rod, with the absence of pre-tension, it is noted that the longitudinal velocity satisfies the Klein–Gordon equation. For full vector problems, corresponding to an elastic chiral rod with pre-tension, time-harmonic Green’s matrix functions are derived for the case of large values of the gyricity parameter. This case is especially interesting because of the presence of both exponentially localised and oscillatory terms in the representation of Green’s matrix components.