Coupled mode theory for nonlinear piezoelectric plate vibrations

摘要

Coupled-mode equations were developed for thickness-longitudinalnvibrations of piezoelectric plate resonators. The equations describe thenresonator as a parametrically excited nonlinear vibrational system withntwo degrees of freedom. Thus one can examine the behavior ofnpiezoelectric resonators from a nonlinear dynamic point of view. In thenpresent paper the derivation of the equations is given. As an example ofnthe application of the equations, the behavior of the resonator in thenvicinity of primary resonance is discussed. The method of multiplenscales is used to solve the coupled-mode equations. An experiment whichnverises the amplitude-driving voltage relation predicted by the theorynis conducted for LiNbO3 resonators