On the inclusion of structural loading and damping in piezoelectric shunt tuning

Expressions for piezoelectric inductive-resistive shunt tuning to a targeted structure mode are obtained by explicit frequency response functions, derived from a combined short- and open-circuit modal representation that accounts for inherent structural damping. The influence of external loading is further included by accounting for the short-circuit dynamic and quasi-static contributions from modes below and above the target mode, respectively. This augmented representation provides accurate frequency response for displacement and electric charge and voltage, and thus be generally used to derive desired shunt tuning strategies. Presently, explicit tuning expressions are based on a flat plateau condition in the voltage amplitude for a parallel inductive-resistive shunt or the charge amplitude for the corresponding series shunt. The tuning robustness with respect to changes in structural damping and external load distributions is verified by a numerical benchmark problem, which further shows that the explicit frequency response functions precisely predict the full structural and electric response around the targeted structure mode. This result can help bypass the need for heavy computations on the full dynamic problem, provide insight into how structural damping and external loading affect shunt tuning and better describe the effective dynamic capacitance, evaluated as the frequency dependent charge-to-voltage ratio.