Electrical tuned vibration absorber: Application of the equal-peak method to linear and non-linear rl piezoelectric shunts

Mechanical tuned vibration absorbers (MTVAs) are devices used to mitigate the vibrations of a structure around one of its eigenfrequencies. By introducing an additional degree of freedom in the structure, MTVAs allow to split the peak of interest in the frequency response in two peaks with lower amplitudes. The design of MTVAs is usually based on the (approximate) equal-peak method proposed by Den Hartog. A closed-form exact solution was however obtained by Asami and Nishihara, for which the two peaks of the frequency response have exactly the same amplitude. Similarly to MTVAs, piezoelectric tuned vibration absorbers (PTVAs) allow to damp efficiently a specific peak of the frequency response. Although a pole placement technique can be used to design such devices, tuning rules are usually based on approximate equal-peak methods which define the optimum values of the resistor and the inductance of the shunt. Very recently, Asami and Nishihara's exact solution has been extended for the equal-peak method to PTVAs by the authors of the present paper. The first contribution of this paper is to illustrate this new optimum design of a series RL piezoelectric shunt on a realistic example. A clamped-free steel plate excited with two piezoelectric actuators and shunted with two piezoelectric transducers is modelled using plate elements (laminates). Non-linearity is then introduced in the host structure, and a new non-linear PTVA for mitigating the vibrations of the non-linear host structure is proposed. The improvement of damping performances in the presence of structural non-linearties using a non-linear PTVA is illustrated.