Nonreciprocal rotating waves and energy-balanced modes in odd elastic circular domain

Abstract

Nonreciprocal linear elastic responses in active systems are described by the non-Hermitian elasticity tensor, referred to as odd elasticity. Existing studies have focused on the propagation characteristics of waves in infinite domains and the skin effects at the boundary, while the dynamics of odd elasticity in geometries with rotational symmetry remain unclear. In this work, we develop a dynamic model for odd elastic circular domain in polar coordinates and derive the wave solutions. We report a novel type of nonreciprocal rotating wave in rotationally symmetric geometries. This phenomenon is characterized by invariant modes, with amplitude either increasing or decaying depending on the direction of propagation. Furthermore, we demonstrate that when the gain and loss induced by two independent odd elastic effects are balanced, the system generates rotating waves with constant amplitude and chiral modes. These findings provide a foundation for the study of nonreciprocal angular momentum transfer and chiral mechanical resonators.