In-plane vibration characteristics of metamaterial plates with locally resonant microstructures

In this paper, in-plane vibration characteristics of square metamaterial plates, which are made of three-dimensional periodic arrangement of the coated spherical particles embedded in a matrix, are investigated theoretically. First, the effective material properties of the plates, including elastic constants and mass density, are obtained by using a simple homogenization method. Then, the governing equations of in-plane vibration are derived and solved analytically for simply supported boundary conditions. In addition, to verify the proposed formulations, the resonance frequencies and corresponding mode shapes of the plates are calculated via commercial finite element method software. Then, a parametric study is performed to illustrate the effects of the geometrical and material properties of the unit cells on the frequencies of metamaterial plates.