The eigenvalue problem and its relevance to the optimal configuration of electrodes for ultrasound actuators

Usually piezoelectric actuators operate in resonance mode, and to achieve the modal shape needed, it's necessary to obtain the exact dislocation of excitation zones. In order to use an actuator for ultrasonic devices, it must meet specific requirements for contact point movement, i.e., the trajectory of a contact point must have elliptical form. Changing geometrical parameters of dynamical structures can maximize effective work. Such kind of simulation leads to an unstable sequence of structural modal shapes, i.e., the structure of the same shape but different geometrical parameters has a different sequence of the modal shapes. Problem arises when we try to automate the actuator modelling process. Solution of the problem usually doesn’t converge, and the numerical analysis becomes meaningless.This paper presents a study of optimizing electrodes dislocation of ultrasonic actuators. The following conditions of optimization problem are considered: to unify excitation voltage forms, to achieve reverse motion and the maximum coefficient of efficiency. Finite element method modelling is performed in calculation process. The results of calculations for the piezoelectric drive are shown for two options of fixing conditions.