Complex Band Structure of 2D Piezoelectric Local Resonant Phononic Crystal with Finite Out-Of Plane Extension

Abstract

In this study, a new type of 2D piezoelectric phononic crystal with a square hollow and convex structures is designed and established. A theoretical study of the piezoelectric phononic crystal is presented in this article to investigate the transmission properties of waves in terms of complex dispersion relations. Based on the finite discretization technique and plane wave expansion, the formula derivation of the real band structure is achieved as well as the complex band diagrams are obtained. The numerical results are presented to demonstrate the multiple broadband complete bandgaps produced by the designed piezoelectric phononic crystal and the propagation characteristics of the elastic waves for different directions. In addition, the transmission loss in the ΓX direction is calculated to verify the band structure. Finally, the effects of the thickness and the square hollow side length on the band structure are discussed.