Generalized modal analysis for closed-loop piezoelectric devices

Abstract

Stress in a piezoelectric material can be controlled by imposing an electrical field. Thanks to feedback, this electrical field can be a function of some strain-related measurement so as to confer on the piezoelectric device a closed-loop macroscopic behaviour. In this paper we address the modelling of such a system by extending the modal decomposition methods to account for the closed loop. To do so, the boundary conditions are modified to include the electrical feedback circuit, hence allowing a closed-loop modal analysis. A case study is used to illustrate the theory and to validate it. The main advantage of the method is that design issues such as the coupling factor of the device and closed-loop stability are simultaneously captured.