COUPLED VIBRATION ANALYSIS OF PIEZOELECTRIC CERAMIC DISK RESONATORS

Abstract

The coupled vibration of piezoelectric ceramic disk resonators was analyzed using an analytical method whilst considering the piezoelectric effect. By introducing a mechanical coupling coefficient, the coupled vibration of the disk resonators was divided into two equivalent vibrations, which are the equivalent longitudinal and radial vibrations. By basing them on piezoelectric and motion equations, the expressions for the admittance of the piezoelectric ceramic disk resonator in coupled longitudinal and radial vibrations were derived, and the resonance frequency equations of the resonator in coupled vibration were obtained. Some important electro–mechanical parameters, such as the electro–mechanical coupling coefficient, were analyzed and their expressions are given when the coupling between the longitudinal and radial vibrations was considered. Some limiting vibrational modes, such as the one-dimensional thickness extensional vibration and the plane radial vibration of thin disk resonators, can be obtained directly from the theory developed in this paper. Experiments were carried out to demonstrate the proposed theory for the coupled vibration of disk resonators. The resonance frequencies of the resonators were measured. It is shown that the measured resonance frequencies are in good agreement with the computed results from the theory and two kinds of resonance frequencies can be obtained, which correspond to the coupled longitudinal and radial vibrations of the disk resonators.