Finite Element Analysis Of High Frequency Vibration Modes Of A Quartz Crystal Plate

The quartz crystal resonators,as the main frequency control component,have been widely used in intelligent devices.The thickness-shear vibration is the functioning mode of quartz crystal resonators.It is very important to understand the distribution of the modes of quartz crystal resonators.It can provide theoretical reference for the design of resonators.Now,the frequencies and mode shapes calculated by straight-crested waves are not completely consistent with the exact vibration modes of quartz crystal resonators and also can not satisfy the need of engineering design of quartz crystal resonators.Although the motion of the quartz crystal resonator can be expressed accurately by the three-dimensional equations of motion and boundary conditions in the piezoelectric medium,it is almost impossible to solve such complex equations.Therefore,Mindlin plate theory is adopted to analyse vibrations of quartz crystal resonators.The computation is performed with a Linux parallel cluster to solve the extremely large scale eigenvalue systems and linear systems.In this thesis,Mindlin plate theory and its finite element implementation are summarized in detail.Firstly,the frequency spectra and mode shapes of the vibrations of quartz crystal plates are obtained.The influence of electrode of quartz crystal plate is also analyzed.The effect of stiffness and mass are considered.The influence of different electrode mass ratio on mode shapes is examined.In order to accurately understand the effects of modal couplings on the performance of a resonator,this thesis calculates the mode shapes to different points.For the circular quartz crystal plates,a new meshing program is used.Frequency spectra and mode shapes of circular plates are obtained.Finally,the mode shapes are compared with the results of commercial finite element software.The results show a good agreement and validate our numerical results.The results of this study show that the finite element method has a significant contribution for the design of quartz crystal resonators.Our finite element program can improve the efficiency of the high frequency vibrations of quartz crystal plates and provides reliable basis for designing products.