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Study of the nonlinear effects on transient process in AT-cut quartz resonators

In this paper, we studied the nonlinear effects arising from large thickness-shear deformation on transient process in an AT-cut quartz crystal plate resonator operating in thickness-shear modes. Based on the Mindlin's plate theory, a system of first-order nonlinear equations of the vibration amplitude evolution was obtained when the evolution amplitude is much slower compared to the high-frequency vibration of the resonator. The amplitude evolution equations were then solved numerically by using the Runge-Kutta method, which results in that in common operating conditions of quartz resonators the nonlinear effect varies from noticeable to significant with the increase of driving voltage. The results obtained are of significant importance for the understanding and consideration in resonator design, especially when resonators are made smaller and thinner in the future.