Shape Optimization of Electrodes for Piezoelectric Actuators Dynamic Analysis

This paper describes a method of shape optimization for electrodes used in piezoelectric actuators. The problem is motivated by recent attempts to develop piezoceramic bimorph actuators that induce changes in two dimensional flow fields. Experimental evidence illustrates that uniformly electroded bimorphs induce undesirable three-dimensional effects into the flow. For the methodology summarized in this paper, both theoretical considerations and numerical experiments are presented. Equations of motion for a typical 2-layer composite transducer(unimorph) structure are presented. The governing equations have been derived via two methods: equilibrium of the force components and the extended Hamilton’s Principle. The systematic derivation of the strong form and weak form of the governing equations is carried out. The objective of the shape optimization problem is to choose an appropriate electrode shape so that the deflection obtained is as large as possible, subject to a fixed electric voltage level, while the plate deflection is made as nearly two-dimensional as possible. Theoretical results for electrode shape optimization are presented for a class of structural dynamics problems. Numerical results for the static analysis are given that illustrate the qualitative behaviors of the approximate methods.