Balanced calibration of resonant piezoelectric RL shunts with quasi-static background flexibility correction

Resonant RL shunt circuits constitute a robust approach to piezoelectric damping, where the performance with respect to damping of flexible structures requires a precise calibration of the corresponding circuit components. The balanced calibration procedure of the present paper is based on equal damping of the two modes associated with the resonant vibration form of the structure, when including a quasi-static contribution from non-resonant vibration modes via a single background flexibility parameter. Explicit calibration formulae are presented, and it is demonstrated by a numerical example that the procedure leads to equal modal damping and effective response reduction, even for rather indirect placement of the transducer, provided that the correction for background flexibility is included in the calibration procedure.