Vibration optimization of an infinite circular AT-cut quartz resonator with ring electrodes

This paper presents the thickness-shear (TSh) vibration modes of an infinite circular AT-cut quartz resonator with ring electrodes. By application of 2D scalar differential equations derived by Tiersten and Smythe, we obtain the resonant frequencies and vibration amplitude distributions of thickness-shear modes in the resonator. The theoretical results have been verified in commercial FEM software COMSOL. Through numerical examples, we illustrate that the distribution of displacement fields in the center part of the ring electrode is adjustable. Furthermore, we optimize the size of the electrodes and the mass ratio of the electrode to the plate, in order to achieve a nearly uniform displacement distribution and mass sensitivity of the resonator. These results can be a theoretical guidance for design and optimization of sensors based on quartz resonators.