Calibration of multiple shunted piezoelectric transducers with correction for residual modes and shunt interactions

Piezoelectric shunt damping can be used for efficient vibration mitigation of a single or multiple vibration modes of a structure. Several analytical tuning expressions have been derived for numerous circuit topologies for a single shunt. However, when multiple shunted piezoelectric transducers are attached to a flexible structure, their individual interactions alongside the spill-over from residual modes affect the calibration accuracy. In this paper, explicit correction terms that represent these effects are presented for multiple shunted piezoelectric transducers targeting a single vibration mode. The correction terms are obtained from the evaluation of effective electromechanical coupling factors, while proper balancing between shunts follows from an assumed proportionality between shunt forces. The proposed correction method is applicable to general shunt architectures, for which tuning is available when targeting a single-degree-of-freedom structure. Its ability to regain nearby optimal damping properties is illustrated numerically for the classic series RL shunt.