Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads

The paper considers optimal design problems in the context of active damping. More specifically, we are interested in controlling the tip-deflection of a cantilever beam subjected to static and time-harmonic loading on its free extreme. First, the thickness profile of a piezoelectric bimorph actuator is optimized and second, the width profile. In the thickness study, formulation and results depend on whether the electric field or the applied voltage is kept constant. For the latter case we propose a differentiable model that connects electric field and piezo-actuator thickness to include electric field breakdown. Results are presented for both design variable cases, for static as well as for dynamic excitation for single frequency and frequency intervals.