Topology optimization of flextensional piezoelectric actuators with active control law

This work deals with the concept o topology optimization method applied to the design of a flextensional piezoelectric actuator (FPEA) targeting vibration attenuation of its dynamic response. On these actuators the piezoceramic shape is usually fixed and it is more advantageous to optimize the host structure topology. The flextensional actuator is formed by two piezoceramic layers that act as a sensor and an actuator coupled with a constant gain active velocity feedback control law (AVFC). The AVFC introduced to the model acts by modifying the damping matrix according to the measurements of the state variables of the system in time-domain. The dynamic equation analyzed throughout the optimization procedure is fully described and implemented, with no simplification for the piezo-ceramic intermediate nodes, what is denominated as the non-collapsed nodes (nc-nodes) model. The dynamic response for the rectangular four-noded finite element analysis is obtained by the Newmark's time-integration method, which is applied to the physical equation and to the adjoint equation needed for the sensitivity analysis. A gradient-based optimization method is applied to minimize the response signal energy of the FPEA under a transient mechanical load. Results are obtained for different control gain values to evaluate their influence on the final topology. The optimized host structure material topology for the nc-nodes model is compared with the collapsed nodes (c-nodes) model. In addition, the nc-nodes model is useful to future developments that intends to provide an external circuit to this FPEA structure aiming to intensify the AVFC damping effect.