A Broadband Energy Harvester with Three-to-One Internal Resonance

In this study, we present a novel two-degree-of-freedom (TDOF) nonlinear energy harvester with internal resonance. To show the performance, a TDOF nonlinear electromagnetic harvester is designed and the mathematical model is derived. The electromechanical coupling system is solved by adopting the harmonic balance method, and the first-order harmonic solutions of the system are provided. The displacement and current frequency response curves are created along with the modulation equations. The advantage of the proposed harvester is that compared to the conventional single-degree-of-freedom (SDOF) nonlinear model and the corresponding TDOF linear system, the results achieve that the proposed scheme can enhance the bandwidth of the harvesting energy. The influences of different excitation amplitudes \({f_1}\) and \({f_2}\) on the response are discussed. The accuracy of the analytical first-order harmonic results is demonstrated by numerical simulations, and the existence of multiple periodic solutions for time history at the same external force frequencies is quantitatively proved.