Common piezoelectric resonators such as the quartz resonators have a very high Q and ultra stable resonant frequency. However, due to small material nonlinearities in the quartz crystal, the resonator is drive level dependent, that is, the resonator level of activity and its frequency are dependent on the driving, or excitation, voltage. We study this phenomenon using the Lagrangian nonlinear stress equations of motion and Piola-Kirchhoff stress tensor of the second kind. The third order nonlinear elastic constants are employed. Solutions are obtained using FEMLAB for the AT-cut quartz resonator and the results are compared with experimental data. The effects of the drive level on typical AT-cut quartz resonators are demonstrated.
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