Piezoelectric frequency up-conversion harvester under sawtooth wave excitation

This work studied an impact based frequency up-conversion mechanism via discontinuous dynamics analysis. The mechanism consists of a piezoelectric beam and a moving stopper. The moving stopper is excited by a sawtooth wave and impacts with the piezoelectric beam, which makes the beam vibrate with its national frequency repeatedly. In the system complex dynamics are induced by impacts, hence to better understand the energy harvesting performance of the piezoelectric beam, we first seek the periodic motions of the system. As the system parameters vary, the output voltage and power of the piezoelectric beam with periodic motions were obtained. The piezoelectric beam was modeled as a mass-spring-damper system, and the linear piezoelectric constitutive law was used to obtain the lumped model of the piezoelectric beam. Using discontinuous dynamics analysis, the generated power and voltage were obtained, and the effect of frequency-up-conversion was demonstrated by comparing the generated power of two cases at low excitation frequencies: (1) the piezoelectric beam was excited via impact with the stopper and (2) the piezoelectric beam was directly subjected to the sawtooth wave. In order to better understand the energy harvesting performance of the piezoelectric harvester, the stable and unstable periodic motions were obtained. The bifurcation diagram of the period-1 and period-2 motions were studied analytically with varying excitation frequency and the initial distance between the stopper and the beam.