Design method of negative capacitor circuit for piezoelectric shunt damping in the presence of parasitic resistances

The parasitic resistances of a piezoelectric element have been often neglected in the conventional analysis of a piezoelectric shunt damping system. This paper indicates that the parasitic resistances cause instability in the piezoelectric shunt damping system with a simple negative capacitor circuit by both numerical simulations and mathematical analysis based on the Routh-Hurwitz stability criterion. This paper then proposes a new two-step design procedure for a modified negative capacitor circuit by taking account of the parasitic resistances. The negative capacitance and the resistance in the circuit are firstly designed based on the fixed-points theory of tuned mass damper, and then, the negative resistance in the circuit is adjusted based on the pole placement technique. The effectiveness of the proposed method is demonstrated by the damping experiments.