The finite element analysis of quartz crystal resonators with nonlinear plate equations

Abstract

The finite element analysis of quartz crystal resonators has been gradually adopted in the design and product improvement for the advantage in predicting the vibration frequency, energy trapping, and calculation of device properties. The analysis can be done with 3D theory of elasticity or piezoelectricity or the Mindlin plate theory by general purpose software or custom development, which has the advantage of reducing the size of analysis significantly for typical thickness-shear vibrations of quartz crystal plates. While linear finite element analysis are adequate for the vibration frequency and frequency-temperature relations, further analysis on important phenomena and electrical parameters require the consideration of nonlinear material properties of quartz crystal. The finite element analysis of quartz crystal resonators has been making great contribution to the design and improvement facing the fast shrinkage of resonator size and elevated precision requirements. The full advantage of the finite element analysis can be taken if electrical parameters and performance behavior can be predicted with the improved analytical model and consideration of nonlinear material properties. The current approach based on the nonlinear theory will meet these objectives since the advantage of the finite element analysis on parallel platforms have been well understood and widely implemented. Our nonlinear analysis will utilize the nonlinear Mindlin plate theory and provide important and essential details on the nonlinear behavior of quartz crystal resonators.