Simultaneous optimization of piezoelectric actuator topology and polarization

This article addresses the problem of piezoelectric actuator design for active structural vibration control. The topology optimization method using the Piezoelectric Material with Penalization and Polarization (PEMAP-P) model is employed in this work to find the optimum actuator layout and polarization profile simultaneously. A coupled finite element model of the structure is derived assuming a two-phase material, and this structural model is written into the state-space representation. The proposed optimization formulation aims to determine the distribution of piezoelectric material which maximizes the controllability for a given vibration mode. The optimization of the layout and poling direction of embedded in-plane piezoelectric actuators are carried out using a Sequential Linear Programming (SLP) algorithm. Numerical examples are presented considering the control of the bending vibration modes for a cantilever and a fixed beam. A Linear-Quadratic Regulator (LQR) is synthesized for each case of controlled structure in order to compare the influence of the polarization profile.