Nonlinear Dynamic Response of Galfenol Cantilever Energy Harvester Considering Geometric Nonlinear with a Nonlinear Energy Sink

The nonlinear energy sink (NES) and Galfenol material can achieve vibration suppression and energy harvesting of the structure, respectively. Compared with a linear structure, the geometric nonlinearity can affect the output performances of the cantilever beam structure. This investigation aims to present a coupled system consisting of a nonlinear energy sink (NES) and a cantilever Galfenol energy harvesting beam with geometric nonlinearity. Based on Hamilton's principle, linear constitutive equations of magnetostrictive material, and Faraday's law of electromagnetic induction, the theoretical dynamic model of the coupled system is proposed. Utilizing the Galliakin decomposition method and Runge-Kutta method, the harvested power of the external load resistance, and tip vibration displacements of the Galfenol energy harvesting model are analyzed. The influences of the external excitation, external resistance, and NES parameters on the output characteristic of the proposed coupling system have been investigated. Results reveal that introducing NES can reduce the cantilever beam's vibration while considering the geometric nonlinearity of the cantilever beam can induce a nonlinear softening phenomenon for the output behaviors. Compared to the linear system without NES, the coupling model proposed in this work can achieve dual efficacy goals over a wide range of excitation frequencies when selecting appropriate parameters. In general, large excitation amplitude and NES stiffness, small external resistance, and small or large NES damping values can achieve the effect of broadband energy harvesting.