Xh. Li et al., COUPLED-MODE THEORY FOR NONLINEAR PIEZOELECTRIC PLATE VIBRATIONS, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 45(3), 1998, pp. 800-805
Coupled-mode equations were developed for thickness-longitudinal vibra
tions of piezoelectric plate resonators. The equations describe the re
sonator as a parametrically excited nonlinear vibrational system with
two degrees of freedom. Thus one can examine the behavior of piezoelec
tric 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 vic
inity of primary resonance is discussed. The method of multiple scales
is used to solve the coupled-mode equations. An experiment which veri
fies the amplitude-driving voltage relation predicted by the theory is
conducted for LiNbO3 resonators.