Multiple band gaps of a ferroelectric based 2D-phononic crystal slab

In this work, we study the band gap properties of a two-dimensional phononic crystal composed of a hexagonal cavity inside a circular enclosure embedded in a homogeneous matrix. A simple two-dimensional structure with a cavity that is modeled with an opening in one side that allows air to enter was studied theoretically using the finite element method (FEM). The properties of acoustic wave propagation in a phononic crystal consisting of periodic inclusions with a cavity placed in an air host material are analyzed. The phononic crystal dispersion relations, transmission loss spectrum, and displacement fields of the eigenmodes of this phononic crystal are investigated. The pressure field distribution inside the domain is solved parametrically through a two-dimensional acoustic wave equation in the horizontal plane as a function of frequency. We have found that several complete band gaps with a variable bandwidth exist for the acoustic waves of longitudinal polarization.