A static analogous circuit for a circular piezoelectric unimorph transducer and its low-frequency radiation impedance

The circular piezoelectric unimorph transducer comprises a substrate, usually a metal plate, upon which is bonded a piezoelectric dielectric layer of a smaller diameter which 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 static displacement and induced voltage of the unimorph as a pressure sensor under uniform pressure as well as the static displacement and induced charge of the unimorph as an actuator due to an applied voltage. Low-frequency analogous electrical circuits are developed for a pressure sensor and actuator. In the case of the actuator, the far-field pressure and radiation impedance are derived for low-frequencies. Plots are shown for displacement vs radial distance, displacement at center vs torsional stiffness, and radiation impedance. The former is compared to a finite element model.