Directionality of wave propagation and attenuation in plates with resonant shunting arrays

This article proposes an analytical method to evaluate the propagation constant in arbitrary direction in the plate with shunting arrays, which can circumvent the complicated transcendental eigenvalue problem. Based on this method, the directionality of waves propagating or decaying in the plate with arrays of resonant shunts is examined, including directionality of attenuation constant, location of band gaps, and group velocity in pass band. Moreover, the theoretical results are verified by simulation in well-accepted commercial finite element software.