Bursting oscillation phenomenon and efficiency analysis of a piezoelectric energy harvester in rotational motion by low-frequency excitation

In this article, the bursting oscillation and energy harvesting efficiency of a piezoelectric energy harvester (PEH) in rotational motion by low-frequency excitation are investigated. On the basis of the slow-fast analysis method, the periodic external excitation term is taken as a slow variable and the control parameter to regulate the dynamic behavior of the fast subsystem. The time history, phase and transformed phase diagrams of the PEH system in some cases when the bursting oscillation occurs are derived. The bifurcation mechanism and motion law are then revealed. Next, the effect of excitation frequency on periodic motions is studied through ω - x bifurcation diagrams. Then, the critical values of the excitation amplitude for bursting oscillations are observed. Afterwards, the influence of cantilever beam equivalent damping ratio on the output voltage when bursting oscillation happens is discussed. Taking the average output voltage value as a measurement index, combining with the variations of the output power with load resistance, the effects of excitation amplitude and frequency on energy harvesting efficiency are analyzed. The results show that the rise of amplitude can widen the frequency band of high energy harvesting efficiency; The frequency near the bursting frequency provides large output power in an instant. Finally, the relationship between the barrier height and bursting oscillation is discussed. It is shown that there exist more than one critical excitation amplitudes for the occurrence of bursting oscillation in some cases of the tristable PEH system. Overall, combining with the external excitation term, potential energy functions and various electromechanical factors, we theoretically analyze the effects on bursting oscillation and energy harvesting efficiency, which provides a reference for the reliability design of multistable piezoelectric energy harvesters.