Numerical effective formulation for guided wave propagation in a metamaterial plate with anisotropic mass density

A numerical method for obtaining the effective anisotropic mass density of elastic composite with arbitrary periodic microstructure is presented and the effective anisotropic mass density is proved to be a second-order tensor. Using the proposed method, a new metamaterial plate with strong anisotropicity in mass density is obtained. Using 3-D elasticity theory, the metamaterial plate is modeled as a continuum medium with obtained effective material properties. The accuracy of the continuum model was evaluated by comparing the dispersion curves with those obtained by exact finite element analysis. Moreover, mode coupling and level repulsion in the anisotropic metamaterial plate are discussed. Finally, preferential directions of wave propagation and energy flow are studied through the comparison of the difference between the phase velocity and group velocity directions.