High-Frequency Vibration of Beveled Crystal Plates by Using Subregional Geometric Fitting Method

The high-frequency vibrations of AT-cut beveled quartz resonators are studied in this work based on Mindlin's theory and Subregional Geometric Fitting Method (SGFM). Quartz crystal plates with nonuniform thicknesses are partitioned into three regions and fitted in each region by using the polynomial functions and the measured geometric morphology data. The governing equations obtained are based on Mindlin's two-dimensional theory and the coupled vibrations are further solved using the partial differential equation module of COMSOL. In numerical calculations, we compared the results of SGFM with the those of global fitting method. The accuracy and effectiveness of the SGFM were also verified. It is has found that the frequencies obtained through the SGFM are slightly higher than the frequencies obtained through the global fitting method. Meanwhile, as the beveling time increases, the frequency increases and the energy trapping effect becomes more obvious. The proposed method can significantly improve the computational efficiency of thickness-shear vibration while ensuring accuracy, and is expected to provide a new geometric fitting method for the analysis of beveled quartz crystal resonators.