Equivalent circuit of an in-plane torsional piezoelectric ring with spiral interdigitated electrodes

Circular piezoelectric elements with torsional vibration abilities are widely utilized as electromechanical transducers in various ultrasonic devices. In this paper, in-plane torsional vibration of a piezoceramic ring with spiral interdigitated electrodes is studied theoretically and numerically. Design of the electrodes and working principle of the ring are described. Mechanical and electrical models of the vibration are derived and the corresponding equivalent circuit is presented. Resonant frequencies of the in-plane torsional vibration with different boundary conditions are calculated. Trends of the resonant frequencies as a function of the ring ratio are investigated. The results are useful for the further optimization of the proposed piezoelectric element in potential applications.