Topology optimization of piezoelectric macro-fiber composite patches on laminated plates for vibration suppression

This work presents a new methodology for the topology optimization of piezoelectric actuators in laminated composite structures with the objective of controlling external perturbation induced by structural vibrations. The linear-quadratic regulator (LQR) optimal control technique is used and the topology optimization is formulated seeking to find the optimum localization of the macro-fiber composite (MFC) active piezoelectric patch by means of the maximization of the controllability index. For the structural model, we propose a simplified MFC/structure interaction model. It is assumed that the MFC is one of the orthotropic material layers with an initial strain arising from the application of an electric potential. This strain acts on the remainder of the structure and its effect is considered analytically. Numerical results show that the proposed MFC structure interaction model presents good agreement with experiments and numerical simulations of models that take into account the electromechanical effect. Results of the actuator location optimization show that the implemented technique improves the structural vibration damping. Results and comparisons are presented for the vibration control strategy using the LQR controller.