Bifurcation behaviors and bursting regimes of a piezoelectric buckled beam harvester under fast-slow excitation

In this manuscript, considering a piezoelectric buckled beam system under fast-slow excitation, the energy harvesting with bursting regimes is discussed analytically and numerically. For the fast sub-system, the averaging process with the generalized harmonic balancing method shows that pitchfork bifurcations will result in small amplitude buckled configurations and large-amplitude configuration centering around the trivial branch. Meanwhile, folds of cycle initiate additional coexisting branches. The structures of the numerical bifurcation diagram are consistent with the analytical results. Moreover, when the amplitude of the fast excitation is relatively large, long-term chaotic transients can be observed. Considering two cases of low-frequency excitation, i.e., the quasi-static one and non-static one, the corresponding bursting patterns are discussed. For the quasi-static case, the fast-slow analysis shows that the fractal basin of the fast sub-system evokes the snap-through transition of the fast-slow flow. Particularly, when the fast sub-system possesses strong transients, the fast-slow flow presents distinct long-term snap-through behaviors. While for the non-static case, the motions of the fast-slow flow are totally dominated by the transient effects. Analysis about the averaged output power shows that introducing the low-frequency excitation to the buckled beam harvester can help broadening the output bandwidth. Moreover, when the transient effects of the fast sub-system are relatively weak, the non-static slow excitation always provides better output performance. However, if the fast sub-system possesses strong transients, there exists a band within which the quasi-static slow excitation provides higher output power.

Automated summary

This paper analytically and numerically investigates the energy harvesting with bursting regimes in a piezoelectric buckled beam system under fast-slow excitation. The study reveals pitchfork bifurcations and folds of cycle in the fast sub-system, which result in small amplitude and large amplitude buckled configurations. The numerical bifurcation diagram is consistent with the analytical results. Long-term chaotic transients are observed when the amplitude of the fast excitation is relatively large. The study also discusses the bursting patterns under low-frequency excitation, both in quasi-static and non-static cases. The averaged output power analysis suggests that introducing low-frequency excitation can broaden the output bandwidth and non-static slow excitation provides better performance in the presence of weak fast sub-system transients. However, a band exists where quasi-static slow excitation provides higher output power when the fast sub-system has strong transients.