Periodic Solutions of an Impact-Driven Frequency Up-Conversion Piezoelectric Harvester

Abstract

Frequency up-conversion has been proved to be an effective approach to increase the output power of a piezoelectric energy harvester (PEH). The proposed system can convert low-frequency vibration from ambient sources to the resonant vibration of the PEH hence can improve the output power efficiency. Frequency up-conversion technologies are introduced via impact or nonimpact magnetic forces to initiate the repeated free oscillations of the piezoelectric generator. No matter impact- or nonimpact-driven PEHs, most studies focus on either finite element simulation or experimental demonstration of PEHs electric power generations. Few, if any, study the effects of the impact-induced discontinuous dynamics on power generation efficiency. In this work, the energy harvesting performance of a piezoelectric beam upon interaction with a softer driving beam was studied. The discontinuous dynamics behind this impact-driven PEH was investigated, and strategies exploited to further improve the power efficiency of the frequency up-conversion process. Based on the linear elastic and linear mechanical-electrical constitutive laws, the lumped parameter models were built for both the driving beam and the piezoelectric driven beam. The numerical solution of the output power is obtained based on the vibration amplitude, frequency, and the electrical load. The soft beam is subjected to a sinusoidal base excitation, and the piezoelectric beam was excited via impacting with the soft driving beam. Based on the discontinuous dynamics theory, the performance of the energy harvesting of the impact-driven system was studied for period-1 and period-2 motions. Based on the stability and bifurcation analysis of periodic solutions, bifurcation diagrams of impact velocities, times, displacements and harvested power versus the frequency of the base excitation were also obtained, and compared to the power generation of a piezoelectric beam with base excitation.