The Vibration of Piezoelectric Plates

Abstract

The characteristic frequencies of infinite piezoelectric plates vibrating between the grounded electrodes of a plane parallel condenser have been rigorously investigated. It is found that the frequencies depend on the piezoelectric constants as well as the elastic constants of the crystal. The effective elastic constants for a piezoelectric crystal do not in general satisfy the same symmetry relations as the true elastic constants. For odd harmonics, which are the only modes which can be excited by a uniform electric field, the strain does not vanish at the surface of the plate for a finite gap between the electrodes. Consequently, the frequencies of free vibration also depend on the separation of the electrodes, and the rigorous theory shows this dependence should not be linear as hitherto supposed. The effect of the gap decreases as the square of the harmonic number and hence the higher frequencies of vibration are not exactly harmonics of the fundamental.