In this work, an impact based frequency up-conversion mechanism is studied via discontinuous dynamics analysis. The mechanism consists of a moving stopper and a piezoelectric beam. The repeated free vibration of the piezoelectric beam achieved through the impaction between the stopper and the beam, With the stopper excited by a sawtooth wave. Due to the impact, the system contains complex discontinuous dynamics, hence to better understand the energy harvesting performance of the piezoelectric beam, we seek the simple periodic motions of the system. As the system parameter varies, the output voltage and power of the piezoelectric beam with periodic motions is obtained. These results were also compared with those obtained when the piezoelectric beam is directly subjected to the same sawtooth wave.
The piezoelectric beam was modeled as a mass-spring-damper system, and the linear piezoelectric constitutive equations have been used to obtain the lumped model of the piezoelectric beam. In this study, numerical solutions of the generated power and voltage were obtained via discontinuous dynamics analysis. When the excitation frequency is low, the effect of frequency-up-conversion is demonstrated by comparing the generated power of two cases: piezoelectric beam excited via impact and beam directly subject to the sawtooth wave. The stable and unstable periodic motions and bifurcation trees of the impact parameters are predicted analytically versus varying excitation frequency for period-1 and period-2.
Simulations of sawtooth-wave adiabatic passage with losses