Dynamic analysis and ℋ ₂ optimisation of a piezo-based tuned vibration absorber

In this article, a piezo-based tuned vibration absorber is proposed and theoretically analysed. The proposed device consists of a proof mass, a piezoelectric actuator and a resilient element (spring). An equivalent mechanical model where the piezoelectric element is connected to a general circuit composed of a resistor, an inductor and a capacitor in series ( RLC) is presented to illustrate the coupling of the electrical components with the mechanical systems. Based on the mechanical replacement model, a C or L circuit can be used to realise a piezo-based tuned vibration neutraliser, while with an RC or RL circuit the piezo-based tuned vibration absorber can be considered as a piezo-based tuned mass damper. For the C and L circuits, tuning strategies are derived to adjust the shunt capacitance and inductance to track the disturbance frequency. In the case of RC and RL shunt circuits, an ℋ ₂ optimisation criterion is used for tuning the piezo-based tuned mass damper. Closed-form expressions for the optimal tuning parameters are provided in this article.