Finite Element Analysis Of AT Cut Quartz Crystal Resonator With The Packaging Structure

With the continuous development of industrial intelligent technology,the performance requirements of quartz crystal resonators are becoming increasingly high on online monitoring system,in terms of the accuracy,precision and stability of devices.The existing studies of quartz crystal resonators mostly are based on Mindlin plate or Lee plate theory,focusing on calculation of resonant frequency and the main performance parameters.The analytical solutions can be obtained by simplifying the problem,but for the high frequency fundamental,third-order overtone,fifth-order overtone and other high-order overtone resonators,the exact analytical solution is very difficult to obtain.For many decades of the development of quartz crystal resonators,the existing research is mainly based on straight-crested wave assumption under quasi-static conditions,which ignoring the vibration modes of the width direction.But this design method can easily lead to the neglect of spurious modes in the width direction,which is not enough to satisfy the practical product requirements.In the design of quartz crystal reasonator products,designers combine the technical experience with experimental data,and the use of finite element software for optimal parameters.In this thesis,the first-order Mindlin plate theory is used to analyze the vibration of rectangular quartz crystal plates,and solutions of the thickness-shear mode,flexural mode and the face-shear mode are obtained.In order to study the influence of spurious modes on vibration of the quartz plates,with the COMSOL software for the cases of couplings of three modes and five modes,we obtained the displacements of the center line along the length and width direction of the plate.With the script file for the applications of COMSOL and MATLAB simultaneous simulation,the ratios of length to thickness and width to thickness are considered for the calculations of frequency spectra,and these data indicated that the results of finite element analysis match existing data well.In addition,this thesis considered packaging structures of quartz crystal resonators with parameters,such as electrode sizes,and locations of conductive glues cover of quartz crystal resonators,which have influences on the resonant frequency and thickness-shear mode of quartz crystal resonators.Based on the Mindlin plate theory,considering the above variable factors,a detailed analysis of the impact of these variables on the vibrations is performed,and the results provide a significant guide for parameter optimization in the design of quartz crystal resonators.