Frequency spectrum of localized vibrations of piezoelectric resonator

The paper addresses the frequencies /spl omega//sub kln/ of localized vibrations of a piezoelectric resonator accounting for the nonequidistance of spectrum by squared frequency. The formulas obtained for /spl omega//sub kln/ with high accuracy (/spl sim/10/sup -4/-10/sup -3/) describe the vibration frequencies of an AT-cut quartz crystal resonator, which were observed experimentally. The influence produced by the electrodes boundaries on the frequency spectrum has been studied.