In order to understand the dynamic characteristics of an ultrasonic motor stator, we proposed a modified two- dimensional axisymmetric finite element model to analyze the three-dimensional vibrational problem of piezoelectric annular and circular plates. In this work, displacement fields are properly assumed and the electric effect is included. Following the finite element method, analyses of axisymmetric and nonaxisymmetric vibration of circular and annular plate, and also the stator of ultrasonic motors can be conducted in a convenient way. Natural frequency, location of contact point and elliptic locus of the stator are then calculated. Effects by different geometry design and selected circumferential wave number are discussed. Comparisons of some typical examples are made between the present work and those available in the literature.

In the present study, effect of satisfying stress boundary conditions, in addition to displacement boundary conditions, in the axisymmetric vibration analysis of circular and annular plates is investigated. A new axisymmetric finite element, which is based on a combination of the conventional displacement-type variational principle and the Reissner¡¦s principle, is proposed. With this formulation, stresses, like displacements, are primary variables, and both displacement and stress boundary conditions can be easily and exactly imposed. Axisymmetric vibration frequencies of some typical circular and annular plates are then obtained with the present approach and are compared with those by the displacement-type axisymmetric finite element. It is found that the conventional finite element, though not satisfying stress boundary conditions, can still obtain sufficiently accurate vibration frequencies of circular and annular plates.