A dynamic analogous circuit for a circular piezoelectric unimorph transducer

The circular piezoelectric unimorph transducer comprises a substrate, usually a metal plate, upon which is bonded a piezoelectric dielectric layer of a smaller diameter that has a conductive coating on the surface that faces away from the plate so that electrical connections can be made to the conductive coating and plate. In this study, the plate has a torsional stiffness boundary conditional at the edge. When the stiffness is zero, the plate is simply supported, and when it is infinity, the plate is clamped. Analytical formulas are derived for calculating the dynamic displacement and induced voltage of the unimorph as a microphone under uniform incident pressure as well as the dynamic displacement and induced charge of the unimorph as a loudspeaker due to an applied voltage as well as the far-field pressure. From these, analogous circuits are created. The matrix used for calculating the coefficients in the displacement equations also yields the eigenfrequencies. Plots are shown for the induced voltage vs frequency as a microphone and the far-field pressure vs frequency as a loudspeaker as well as the electrical impedance. Also, plotted are the results of finite element simulations for comparison together with the sensitivity to the variation of various parameters.