The finite element analysis of high-frequency vibrations of quartz crystal resonator strcuctures

Mindlin plate theory is widely used in the analysis of thickness-shear vibrations of quartz crystal resonators with analytical solutions of frequency and displacements. In the design of resonators, we always want to get accurate solutions for the determination of structural parameters. With complicated boundary conditions and geometry by taking packaging and electrodes into consideration, it will be impossible to solve with the Mindlin plate equations. On the other hand, the finite element method (FEM) with three-dimensional theory of piezoelectricity can efficiently solve such a problem,although earlier studies in the thickness-shear vibrations of quartz crystal resonators with actual model by popular FEM tools such as ANSYS are limited. Analytical modules are used in the analysis of the thickness-shear vibrations of quartz plates in this study, and the curve of fundamental frequency of thickness-shear vibration is obtained by changing the length and width of quartz crystal plates. In the analytical model with supports, through altering the length of plates, radius and the distance between conductive adhesive supports, the frequency curves with different parameters are obtained.