Saturation correction for a piezoelectric shunt absorber based on 2:1 internal resonance using a cubic nonlinearity

Abstract

In this study, we present a theoretical and experimental analysis of an antiresonance detuning correction for a nonlinear piezoelectric shunt absorber based on a two-to-one internal resonance. Thanks to this purely nonlinear feature, the oscillations of the primary system become independent of the forcing at a particular antiresonance frequency, thus creating an efficient reduction of the vibration. Past works of the literature present the design of the piezoelectric shunt and show that it is subjected to a softening behavior that detunes the antiresonance frequency as a function of the amplitude and thus degrades the performance. It is also shown that this softening behavior is caused by some non-resonant terms present in the equations, linked to the piezoelectric coupling. To counteract this undesired effect, we propose in this work to add a cubic nonlinearity in the shunt circuit, in addition to the quadratic one already present. Its tuning is based on a normal form analysis already published, which shows how cubic nonlinearities can cancel the effect of quadratic non-resonant terms. The present article describes the main features of the theory and focuses on the experimental proof of concept of this antiresonance detuning correction as well as the analysis of its range of validity. It is applied to the damping of the first bending mode of a hydrodynamic foil structure.