3-D modeling of hollow cylinder piezoelectric resonator by polynomial approach

The semi-analytical modeling of acoustic wave resonators is discussed in this study. A polynomial approach to wave propagation is used to predict the electromechanical behavior of piezoelectric resonators in a circular ring with hexagonal elastic symmetry. We present a Legendre polynomial-based 3D semi-analytical technique capable of accounting for finite lateral dimensions. Using delta functions, the boundary conditions are immediately integrated into the wave equations. The Legendre polynomial method’s validity is confirmed by comparing polynomial results with finite element method (FEM) results from the literature.