Programmable dielectric metamaterial plates via flexoelectricity and L-C circuits

Abstract

We propose a dielectric metamaterial plate (DMP) like structure consisting of a pure dielectric plate and simple external L-C circuits utilizing the interaction between the flexoelectric-induced polarization field and the l-C circuits. For modeling and predicting wave propagation properties of flexural waves in the proposed DMP structures, we develop a two-dimensional (2D) mixed finite element method (M-FEM) incorporating flexoelectricity and external L-C circuits and also verify its accuracy with the corresponding analytical solutions. The unique wave propagation phenomena including bandgap tuning, wave localization and topological interface state in the proposed DMP structure are examined and manipulated through changing parameters of the electrode pairs and the connected L-C circuits. Numerical results show that altering the length of the electrode pairs and adjusting the connected L-C circuits can flexibly and effectively control wave propagation characteristics of flexural waves in the proposed DMP structures. This paper not only provides a new way for the design of mechanical metamaterials with programable wave properties but also lays the theoretical foundation for modeling multi-field coupling mechanical behaviors of DMP structures coupled with flexoelectricity and external L-C circuits.