The finite element analysis of thickness-shear vibrations of quartz crystal plates with ANSYS

Finite element analysis is a powerful approach to the vibration analysis of complicated structures including the piezoelectric acoustic wave resonators such as the quartz crystal resonators, which usually vibrate at the thickness-hear mode with much higher frequency. The analysis has been done with the Mindlin plate equations for straight-crested wave solutions for displacements and vibration frequency, which are important in the design of quartz crystal resonators. But the spatial distribution of displacements with structural complications such as thickness variation, electrodes, and mountings is hard to obtain. Such solutions will be important to explain the dominant properties of the thickness-shear vibrations in a finite plate such as the frequency variation and displacement confinement, but more accurate solutions for actual resonators can only be obtained with the finite element method, with the sophistication of general purpose finite element software such as ANSYS, ABAQUS, NASTRAN, and lately COSMOL and widely available computing power, the high frequency vibrations of quartz crystal resonators have been studied with these popular and powerful tools. We choose the ANSYS on a Windows based personal computer as the analysis platform, and typical models of quartz crystal resonators with rectangular and circular configurations are created and analyzed. The accurate solutions of displacement distribution can be used in the optimal selection of the structural parameters. Challenges arising from the interpretation of vast amount of data from the finite element analysis are also discussed.