Modal analysis and harmonic response of resonators: An extension of a mapped orthogonal functions technique

A mapped orthogonal functions technique is extended for solving three-dimensional acoustical wave problems with taking into account electrical sources. For validation and illustration purposes, it is applied to the determination of the frequency spectrum of a piezoelectric disc resonator. Formulation is given for the calculation of the electric input admittance along with specializations for open- and short-circuit boundary conditions. In view of validation, normal frequencies and electric input admittance are obtained for specific geometries where a one-dimensional analytical model is working and compared against results from the analytical approach. Illustrative results, dispersion curves for a PZT5A resonator and electromechanical coupling coefficients as a function of the diameter to thickness ratio for the first radial mode of a respectively PZT5A, AlN and SiC resonator are also given.