Influence of Piezoelectric Energy Transfer on the Interwell Oscillations of Multistable Vibration Energy Harvesters

This manuscript investigates the effect of nonconservative electromechanical energy transfer on the onset of interwell motions in multistable piezoelectric energy harvesters. Multistable piezoelectric energy harvesters have been proven to outperform their linear counterparts when they undergo interwell oscillations. The conditions for interwell oscillations in such harvesters are generally characterized in terms of their potential energy function. This is accurate for a stand-alone mechanical oscillator but when the piezoelectric patches and a load resistance are included, a part of the kinetic energy supplied to the system is converted into electrical energy. In this manuscript, the Melnikov necessary conditions for interwell oscillations are derived, considering the effect of this nonconservative piezoelectric energy transfer. Through Melnikov theoretic analysis, it is shown that in a tristable harvester with all the three potential wells having the same depth, a higher excitation level is required to enable exits from the middle well to the outer wells when compared to the exits from the outer wells to the middle well. This is in stark contrast to a stand-alone tristable mechanical oscillator wherein interwell motions are simultaneously enabled for all the wells having the same depth.