Frequency up-conversion is an effective way to increase the output power from a piezoelectric beam, which converts the ambient low-frequency vibration to the resonant vibration of the piezoelectric energy harvesters (PEH) to achieve high electric power output. Frequency up-conversion technologies are realized via impact or non-impact magnetic force to mediate the interaction between the driving beam and the generating beam. Most studies focus on the either linear model prediction or experimental verification of the linear analysis. Few, if any, study the effects of the impact induced nonlinear phenomena on power generation efficiency. In this work, we investigate how to use discontinuous theory to improve the power efficiency of the frequency up-conversion process caused by impacts. The energy harvesting performance of a piezoelectric beam in interaction with a softer beam in periodic motion is studied. The discontinuous dynamical system theory is applied to this problem to study the piezoelectric behavior under periodic motions and its bifurcations.
The beams are modeled with two spring-mass-damper systems, and the analytical model of the piezoelectric beam is created based on the linear mechanical-electrical constitutive law of the piezoelectric material, and the linear elastic constitutive law of the substrate. Based on the theoretical model, the analytical solution of the output power is derived in terms of the vibration amplitude, frequency, and the electrical load. The soft beam is subjected to a sinusoidal base excitation, and the impacts of the more flexible beam excite the piezoelectric beam. The performance of the energy harvesting of period one and period two motions have been studied and bifurcation trees for impact velocities, times, displacements and harvested power versus the frequency of the base excitation are obtained.