This study investigates an impact based frequency up-conversion mechanism via discontinuous dynamics analysis. The mechanism composed of a stopper and a piezoelectric bimorph. The piezoelectric beam is subjected to a sinusoidal base excitation and impacts with the stopper. In this system, complex dynamics are induced by impacts, hence to better understand the energy harvesting performance of the piezoelectric beam, we seek the steady state periodic motions of the system. As the excitation frequency varies, the output voltage and power of the piezoelectric beam with periodic motions were obtained.
The piezoelectric bimorph was modeled as an Euler-Bernoulli beam, and the linear piezoelectric constitutive equations were used to obtain the equations of the piezoelectric beam. The generated voltage and power were obtained using discontinuous dynamics analysis. In order to better analyze the energy harvesting performance of the piezoelectric energy harvester, the stable and unstable periodic motions were obtained. The bifurcation diagram of the period-1 and period-2 motions were obtained analytically as the excitation frequency varying.