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This work presents tuning rules for piezoelectric shunts aiming to mitigate multiple structural resonances. Starting from a specification procedure of the shunt characteristics, the electrical parameters are derived for shunt topologies proposed in the literature, namely Hollkamp’s shunt, the current flowing shunt, the series parallel impedance structure and the current blocking shunt. Effective vibration mitigation of multiple structural modes is demonstrated numerically and experimentally on a piezoelectric beam. Performance in terms of vibration reduction obtained with the different shunts is shown to be comparable if similar shunt characteristics are considered.

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The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low electromechanical coupling are prone to delay-induced instabilities entailed by the sampling procedure of the digital unit. An explicit relation is derived between the effective electromechanical coupling factor and the maximum sampling period guaranteeing a stable controlled system. Since this sampling period may be impractically small, a simple modification procedure of the emulated admittance of the shunt circuit is proposed in order to counteract the effect of delays by anticipation. The theoretical developments are experimentally validated on a clamped-free piezoelectric beam.

This work develops a unified modeling framework for piezoelectric structures controlled by passive shunts connected to a single transducer and/or networks interconnecting multiple transducers. A common tuning procedure for these different control approaches, termed decentralized and centralized approaches, respectively, is proposed. The generic model is then used to compare them in terms of vibration mitigation performance. It is shown that decentralization can be detrimental to performance in general. Digital vibration absorbers are then leveraged to realize the shunts and/or networks. In this regard, the proposed tuning procedure solely relies on characteristics that can be identified from the digital units of these absorbers. The theoretical developments are numerically and experimentally validated on piezoelectric beams.