Transient thickness-shear vibration of a piezoelectric plate of monoclinic crystals

We analyze electrically forced, transient thickness-shear vibration of a piezoelectric plate of monoclinic crystals as an acoustic wave resonator. These crystals include the widely used, rotated Y-cut quartz and langasite crystal plate resonators as special cases. A trigonometric series solution is obtained with which a few transient effects in a piezoelectric resonator under a sudden change or fluctuation of the driving voltage amplitude or frequency are calculated and examined. It is found that under a sudden change of the driving voltage amplitude the transition of the resonator vibration takes about 0.1 s for an AT-cut quartz resonator, and that a 10 Hz deviation of the driving frequency from the fundamental resonance causes a significant drop of the vibration amplitude.