Coupled mode theory for nonlinear piezoelectric plate vibrations

Coupled-mode equations were developed for thickness-longitudinal vibrations of piezoelectric plate resonators. The equations describe the resonator as a parametrically excited nonlinear vibrational system with two degrees of freedom. Thus one can examine the behavior of piezoelectric resonators from a nonlinear dynamic point of view. In the present paper the derivation of the equations is given. As an example of the application of the equations, the behavior of the resonator in the vicinity of primary resonance is discussed. The method of multiple scales is used to solve the coupled-mode equations. An experiment which verises the amplitude-driving voltage relation predicted by the theory is conducted for LiNbO/sub 3/ resonators.