Effect of Electrical Uncertainties on Resonant Piezoelectric Shunting

Resonant piezoelectric shunting is one of the most studied techniques for damping structural vibrations by using piezoelectric transducers in conjunction with passive electric networks. It is based on establishing an internal resonance between a mechanical system and an electrical circuit, which is comprised of a shunting impedance and the piezoelectric inherent capacitance. The problem of analyzing the effect of variations of the electrical impedance with respect to its optimal choice is investigated here. Simple closed-form formulas for quantifying the performance loss due to deterministic variations of the electrical elements are derived, and they are validated through numerical tests. The effect of stochastic perturbations is also considered, manageable formulas are provided, and validated by Monte Carlo simulations. The analyses focus on forced vibrations, and the arising H _∞ optimization problem is solved by making use of fundamental properties of the system transfer function.