A nonlinear piezoelectric shunt absorber with a 2:1 internal resonance: Theory. (1st May 2022) - Shami, Zein A.; Giraud-Audine, Christophe; Thomas, Olivier
Abstract: In this paper, a semi-passive nonlinear piezoelectric shunt absorber is presented, aiming at attenuating the vibration of a resonant elastic structure under external excitation. This is done by connecting the elastic structure to a nonlinear shunt circuit via a piezoelectric patch. The nonlinear shunt circuit consists of resonant circuit that includes a quadratic non-linearity. A particular tuning of the natural frequency of the shunt enables to create a two to one internal resonance. This generates a strong coupling between the mechanical mode and the electrical mode, leading to replace the mechanical resonance with a nonlinear antiresonance associated with an amplitude saturation, thus leading to an efficient vibration reduction. In this paper, we first propose a theoretical model that is expanded onto a suitable electromechanical modal basis and reduced to the two modes of interest, nonlinearly coupled by quadratic terms. Then, analytical solutions are obtained by the multiple scale method and compared to a reference numerical solutions stemming from the harmonic balance method. This enables to investigate the performance of the system in term of vibration absorption as well as giving design rules to tune the nonlinear shunt and to choose the free parameters of the system. Highlights: We propose for the first time a nonlinear piezoelectric shunt damper based on a 2:1 internal resonance. We show that the electromechanical modal coupling is responsible of non resonant terms that have an unusual strong effect on the dynamics. Provided a simple autotuning law, the classical saturation phenomenon of the mechanical mode is demonstrated. An optimization of all parameters and some simple design rules are proposed.