Thickness-Shear Vibrations Analysis And Finite Element Simulation Of Partially Electroded Circular AT-Cut Quartz Plate

Quartz crystal resonator is an electronic component controling frequency. With the fast development of electronic device towards miniaturization, high-frequency and low-power consumption, acoustic wave resonators attract more and more attention for time-keeping, frequency generation and operation. Quartz crystal resonator is the most widely used acoustic resonator, therefore how to improve the quartz crystal resonator frequency stability has become an important topic in the field of acoustic wave devices. In order to improve the frequency stability of quartz resonator, we need to analyze and simulate the working mode and spurious modes of the resonator. The purpose of this paper is to study high frequency thickness-shear vibration of circular AT-cut quartz crystal resonator.This paper mainly studied circular AT cut quartz crystal resonator from two aspects. First, the circular quartz plate is analyzed by the quartz crystal plate theory. Second, the vibration of quartz crystal resonator is simulated by finite element method.Based on the above mentioned, this paper focuses on the thickness-shear vibrations of centrally partially electroded circular AT-cut quartz plate. First, this paper introduces the basic theory of piezoelectric elasticity. Based on Tiersten's two-dimensional theory, the expressions of the thickness-shear vibration frequency for the infinite and finite AT-cut quartz crystal plates are obtained. Through coordinate transformation, the two-dimensional scalar differential equation derived by Tiersten and Smythe is solved by separation of variables in the elliptical coordinate system, which results in the Angular and Radial Mathieu Equation. Combining boundary and continuity conditions, we obtain the exact solutions for vibration frequencies and modes of centrally partially electroded circular AT-cut quartz plates. We also use the method of 2-D and 3-D finite element model for the modeling and analysis of centrally partially electroded circular AT-cut quartz plates and compare the obtainrd results with those from theoretical results.. Finally the influences of electrode layer on the vibration frequencies and modes of quartz plate are discussed in detail.