Force-frequency effects in third overtone thickness shear quartz resonators

摘要

Third overtone and higher overtone thickness shear quartz resonators are used as a frequency source in ultra-stable oscillators. The governing equations for the force-frequency effect and the related acceleration sensitivity of these resonators are well established. The force exerted on the resonator causes initial stress and strain that in turn changes the resonator frequency. However, we have found recently that for accurate force-frequency effects, the calculation of initial stress and strain must include nonlinear material constants and nonlinear geometric displacements. There is a good set of experimental data by Mingins, et. al., and Fletcher, et. al. on third overtone resonators for which until now no analytical models were accurate enough. We present and demonstrate in this paper our finite element models for acceleration sensitivity with nonlinear initial stress and strain that yielded results which compared well with these experimental data.