A few transient effects in AT-cut quartz thickness-shear resonators

We study a few transient effects of AT-cut quartz thickness-shear resonators, including resonator turning on and turning off as well as voltage amplitude and frequency fluctuations. Mindlin's two-dimensional plate equations are used and solved analytically. Both a sudden change and a gradual change of the driving voltage are studied. It is found that for a resonator with a frequency of 1.649430868 MHz and material quality factor of Q = 105, the characteristic time scale of the transient effects is of the order of 0.1 s.