Finite element modelling for a piezoelectric ultrasonic system

In this paper, a three-dimension (3-D) mechanical element with an extra electrical degree of freedom is employed to simulate the dynamic vibration modes of the linear piezoelectric, piezoelectro-mechanic and mechanical behaviors of a metal disc structure embedded with a piezoelectric actuator. In piezoelectric finite element formulation, a discretized equation of motion is developed and solved by using the integration scheme to explain why an adaptive boundary condition, a simple support condition with three non-equal-triangular (120°–90°–150°) fixed points near the edge, which is the asymmetric disc used as the stator of the studied ultrasonic motor, for the mechanical design of an asymmetric disc-type piezoelectric ultrasonic stator, is defined so that a lateral elliptical motion of the contact point between stator and rotor can be realized for driving the rotor. It starts from hybrid elements with displacement and electric potential as the nodal d.o.f.s model and uses Guyan reduction and Householder-Bisection inverse iteration to find the displacement profile and displacement vector flow of the stator under frequency driving. The standing wave existence is also proven by the displacement patterns of the finite element theoretical model.