Utilizing Hertzian contact model for a vibro-impact unimorph bistable energy harvester to increase working frequency bandwidth and harvested power

Abstract

The typical bistable energy harvester (TBEH) systems usually have a limited working frequency bandwidth and low performance in energy conversion. This paper proposed a unilateral vibro-impact piezoelectric cantilever beam energy harvester. The novel vibro-impact bistable energy harvester (VIBEH) improves the drawbacks of a TBEH system. Despite previous research, in this paper, the collision process is modeled by nonlinear Hertzian contact theory. Nonlinear contact law adds strong nonlinearity to the harvester. By using the extended Hamilton principle and Euler-Lagrange equation, the governing equations of the energy harvester are derived and solved numerically. The existing nonlinearities cause frequency leaks and affect the type of motion (inter-well or intra-well motion) by changing the equilibrium points of the system. By applying nonlinear tools like Poincare diagrams, bifurcation plots, and phase portraits, the effects of periodic or chaotic oscillations will be studied on the performance of the VIBEH system. Finally, the effects of barrier stiffness, initial gap, barrier location, and electrical load are determined on the performance of the VIBEH system. The obtained results showed that using the VIBEH system could broaden the working frequency bandwidth by about 71.9%. Furthermore, the optimized values of impacting properties and electrical load are examined.