Non-Hermitian wave dynamics of odd plates: Microstructure design and theoretical modelling

Abstract

The concept of odd elasticity was recently introduced to characterize the elastic behavior of solids that consist of active components, exhibiting an asymmetric elastic modulus tensor. In this paper, we propose, for the first time, the microstructure design of an odd plate, which is composed of a lattice plate with a piezoelectric-patch-based sensor–actuator feed-forward system. By leveraging the nonreciprocal coupling between shear forces and bending curvatures, the odd plate constitutive relation is formulated in the low frequency region, which features as four asymmetric coupling parameters known as “odd parameters”. We reveal that the two-dimensional (2D) odd plates can perform directional wave energy amplification and the amplification angle can be determined analytically through the rotation of coordinate system. We also numerically demonstrate the directional wave amplification phenomena that arise from the optimal combination of odd parameters. In addition, we analytically uncover the presence of Stoneley-like interfacial waves between two plates with two odd parameters in opposite signs, which is further characterized by the numerical simulation. Unlike interfacial waves between topological structures, the interfacial waves between odd plates can exist for any working frequency, enabling the design of some novel waveguides. This research on the control of flexural waves in odd plates could shed lights on 2D non-Hermitian systems in elasticity.