A mechanical analogue of electromagnetic induction for waves in a chiral elastic structure

Abstract

Classical Faraday’s law on electromagnetic induction states that a change of magnetic field through a coil wire induces a current in the wire. A mechanical analogue of the Lorentz force, induced by a magnetic field on an electric charge, is the gyroscopic force. Here, we demonstrate a mechanical analogy with a chiral elastic waveguide subjected to gyroscopic forcing. We study waves in an infinite mass-spring ‘gyrocore helix’, which consists of a helix and a central line (gyroscopic elastic core). The helicoidal geometric chirality is considered in conjunction with a physical chirality, induced by gyroscopic forces. It is shown that the interplay between these two chiral inputs leads to the breaking of symmetry of the associated dispersion diagram, resulting in a unidirectional waveform with the direction of propagation being tunable through the gyricity.