ANALYSIS OF THE EQUIVALENT CIRCUIT OF PIEZOELECTRIC CERAMIC DISK RESONATORS IN COUPLED VIBRATION

Based on the piezoelectric effect and the wave equation, the coupled vibration of the piezoelectric ceramic thick disk resonator is studied when the shearing and torsion are neglected. The coupled vibration of the disk resonator is reduced to two equivalent vibrations, one being the equivalent radial vibration, and the other the equivalent longitudinal vibration. The relation between these two equivalent extensional vibrations is analyzed and the two-dimensional equivalent circuit of the thick disk resonator is derived. Compared with one-dimensional theory, an additional force is produced in the two-dimensional equivalent circuit. It is obvious that this force results from the coupling between the radial and longitudinal vibrations in the thick disk. It is shown theoretically that the resonance frequency of the thick disk in coupled vibration can be computed in an analytical method, and the measured resonance frequencies are in good agreement with the computed results.