Balanced calibration of resonant shunt circuits for piezoelectric vibration control

Shunting of piezoelectric transducers and suitable electric circuits constitutes an effective passive approach to resonant vibration damping of structures. Most common design concepts for resonant resistor-inductor (RL) shunt circuits rely on either maximization of the attainable modal damping or minimization of the frequency response amplitude. However, the former is suboptimal near resonance due to constructive interference of the two modes with identical frequency, and the latter results in reduced implemented damping. This article proposes an explicit pole placement-based design procedure for both series and parallel RL circuits. The procedure relies on equal modal damping and sufficient separation of the complex poles to avoid constructive interference of the two modes. By comparison with existing design procedures, it is demonstrated that the present calibration leads to a balanced compromise between large modal damping and effective response reduction with limited damping effort.