Evaluation of Resonance Intensities and Frequencies for Piezoelectric Partial-Drive Systems Using Application of Mason's Equivalent Circuit and Complex Series Dynamics

Abstract

In order to evaluate the `resonance intensities' and resonance frequencies of piezoelectric transducers driven `partially', two mathematical methods are considered: One is the evaluation of `speed of divergence' at the resonance of Mason's equivalent circuit which is applied appropriately using the conventional concept of a distributed-parameter circuit, and the other is a superposition of complex dynamical variable η to form complex infinite geometric series in which |η|2 corresponds to the stored energy in the transducer and in which the way of superposition reflects the electrical and mechanical boundary conditions of the transducer. The resonance intensity is related to the effective power at the resonance. The `partial drive' can induce resonance modes other than a set of odd-degree modes, with various resonance intensities due to a nondissipative cause, on appropriate boundary conditions. The calculation results of the two methods agree with each other satisfactorily, and thus suggest the physical reasonableness of both methods.