Passive control of multiple structural resonances with piezoelectric vibration absorbers

A novel sequential tuning procedure for passive piezoelectric shunts targeting multiple structural modes is proposed in this work. The control authority on each targeted mode can be quantitatively chosen ab initio and is shown to be limited by passivity requirements, which highlights the fundamental limitations of multimodal piezoelectric shunts. Based on effective characteristics of the piezoelectric system around resonance, electrical damping ratios and resonance frequencies are derived using well-established single-mode formulae from the literature, thereby fully specifying the characteristics of the shunt impedance. The proposed approach is numerically verified and experimentally validated on piezoelectric beams by emulating the shunt with a digital vibration absorber.