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

Abstract

With the fast growth of electronic products such as wireless telecommunication devices and personal computers, quartz crystal resonators are widely used as stable and precise frequency control components. Due to miniaturization of practical product and higher frequency requirements, how to avoid mode coupling which will severely affect product's quality becomes a key problem to be solved during the design stage. However, designers can only adjust the size and shape of quartz plate based on experiences. The Mindlin plate theory can be used to obtain analytical solutions of the straight-crested wave displacements and vibration frequency, but the effects of complex structure such as change of the three-dimensional sizes of the chip, electrodes, packaging and mounting on the quality factor cannot be accurately analyzed by this theory. Therefore, the sophisticated FEM becomes important for this problem. In this study, we employed the general purpose finite element method software ANSYS to analyze the fundamental thickness-shear vibrations of typical rectangular AT-cut quartz crystal plates, and obtained its free vibration frequencies and spatial distributions of displacements which verify known results. Based on these results, we further extended our research to investigate the effect of length of the rectangular plate on the vibration mode, establishing a plate model with conductive adhesive and analyze the impact of the position and the size of adhesive. These studies showed we can adjust these small sizes to enable quartz crystal resonator work in a stable thickness-shear vibration state. Our work is to establish a complete procedure of quartz crystal resonators with ANSYS and form the base of FEM analysis for product design.