Vibration Analysis Of Quartz Resonator With Partially Polygonal Electrode

Airborne electronic equipment is the equipment necessary to ensure the safe flight of aircraft and to complete various missions.Its performance and configuration is one of the important indicators to measure the level of national aviation technology.The quartz crystal resonator is an acoustic wave device made by utilizing the piezoelectric effect of the quartz crystal,and is widely used in aircraft communication systems,navigation systems,and aviation instruments.As airborne electronic devices are in dire need of miniaturization,high frequency,and low power consumption,this requires us to continuously optimize and optimize the performance of the resonator.In this paper,the shape of the electrode of the quartz crystal resonators studied is polygonized,and then the vibration characteristics in the thickness-shear mode are studied.In this paper,we mainly study the vibration problem of the thickness-shear mode of the AT-cut quartz crystal resonator,and consider the case where the upper and lower surface electrodes are regular polygons and homotopy regular polygons.In this paper,the thickness-shear vibration of quartz crystal resonator is analyzed by theoretical calculation and finite element simulation.In the theoretical calculation,based on the two-dimensional scalar differential equation deduced by Tiersten,the displacement solution hypothesis containing the double-triangular series is constructed by the Ritz method,and the complex integral problem in the equation is processed by the Gaussian integral formula.The problem of the number of conditions is solved by the Tikhonov regularization method,and finally the resonant frequency of the thickness-shear modes of the quartz resonator and its corresponding vibration modes are obtained.For the finite element simulation,the PDE module of the finite element software COMSOL is also used to simulate the quartz crystal resonator based on the two-dimensional scalar differential equation.The resonance frequencies and corresponding modes are also obtained.It can be seen from the distribution of the mode shape obtained by the two methods that the thickness-shear vibration of the polygonal or homotopy polygonal AT-cut quartz crystal resonator is concentrated in the electrode region,and this phenomenon is called a trap phenomenon.By comparison,it can be found that the theoretical calculations are basically the same as the results of the finite element simulation,which verifies the correctness of the two methods.