Design and analytical evaluation of an impact-based four-point bending configuration for piezoelectric energy harvesting

Aiming toward improved energy conversion in piezoelectric energy harvesters, this study investigates four-point bending (FPB) energy harvesters (FPB-EH) to explore their prominent features and characteristics. The FPB configuration innovatively extends energy harvesting capabilities relative to conventional cantilever beams. The FPB-EH comprises a composite piezoelectric beam that rests on two supports of a fixed clamp, excited by contact force applied at two contact lines on a moving clamp. A comprehensive analytical electromechanical model for the vibrating energy harvester is presented with unique modeling features, including multi-beam sections and multi-mode-shape functions. Solutions of the analytical model are presented for a wide range of contact force types, including steady-state solutions for harmonic forces, impact forces, periodic and non-periodic arbitrary forces. This comprehensive model progresses the state-of-the-art piezoelectric modeling knowledge and is readily applicable to various energy harvesting configurations. The model is validated against experimental results and finite element analysis. Next, a parametric study was performed to evaluate the effects of various FPB characteristics, including the fixed and moving clamp spans, the waveform, and the period-time of contact force. The results indicate that the FPB configuration can enhance energy conversion efficiency and normalized output energy by factors of over 3 and 6, respectively. Finally, guidance is given for selecting between cantilever and four-point bending configurations.