The piezoelectric resonator in a dc electric field

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Abstract
The influence of the dc electric field ē on characteristic frequencies (f r and f a) of piezoelectric resonators longitudinally vibrating in a weak driving field ē has been considered. The analysis of the equivalent electric circuit of the resonator has been made in the case when the linear dependences f r(ē) and f a(ē) are satisfied. The relation of f r and f r to the linear and nonlinear electromechanical constants of a crystal has been obtained. The possibility of measuring nonlinear dielectric, piezoelectric and electrostrictive coefficients has been shown. The determination of some nonlinear constants has been carried out for KH2PO4, LiJO3, Bi12GeO20 and other crystals.

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