This paper deals with passive monomodal vibration control by shunting piezoelectric actuators to electric impedances constituting the series of a resistance and an inductance. Although this kind of vibration attenuation strategy has long been employed, there are still unsolved problems; particularly, this kind of control does suffer from issues relative to robustness because the features of the electric impedance cannot be adapted to changes of the system. This work investigates different algorithms that can be employed to optimise the values of the electric components of the shunt impedance. Some of these algorithms derive from the theory of the tuned mass dampers. First a performance analysis is provided, comparing the attenuation achievable with these algorithms. Then, an analysis and comparison of the same algorithms in terms of robustness are carried out. The approach adopted herein allows identifying the algorithm capable of providing the highest degree of robustness and explains the solutions that can be employed to resolve some of the issues concerning the practical implementation of this control technique. The analytical and numerical results presented in the paper have been validated experimentally by means of a proper test setup.

This article addresses piezoelectric shunt damping through a resonant shunt associated with negative capacitances. The main objective of this article is to provide guidelines for choosing the best electrical circuit layout in terms of control performance and possible stability issues. This article proposes general analytical formulations for the tuning/optimisation of the electrical shunt impedance and for the prediction of the attenuation performance. These formulations are demonstrated to be valid for all the possible configurations of the negative capacitances. It is demonstrated that the behaviour of the different shunt circuits can indeed be described by a common mathematical treatment. Moreover, the use of two negative capacitances together is shown to provide benefits compared to traditional layouts based on a single negative capacitance. The mentioned advantages relate to both stability and attenuation performance. The use of a resonant shunt with the addition of negative capacitances is finally proven to provide enough attenuation to even cancel eigenfrequency peaks in some cases. This article also analyses the main issues arising from the practical implementation of the negative capacitances. Finally, the theoretical results are validated through experiments conducted on a cantilever beam coupled to two piezoelectric patches.

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