Performance enhancement of a coupled magneto-mechanical harvester through impact

The narrow operational bandwidth inherent to linear systems severely limits their efficacy in real applications, especially with low-amplitude broadband excitations. This paper explores an impact-driven magneto-mechanical system, designed to improve broadband performance. The system is two coupled pendulums with tip magnets and intentional asymmetry. The asymmetry is introduced via a unilateral rigid wall constraint, which induces piecewise physical impacts. The system is modeled using an extended Lagrange formulation and analyzed through a semi-analytical Harmonic Balance (HB) framework. Unlike conventional studies that rely primarily on numerical integration, this work explicitly quantifies the amplitude transfer to sub-harmonic and super-harmonic components during impacts, mapping the system's bifurcations and the emergence of strange attractors within chaotic regimes. This approach uniquely enables the mathematical reconstruction and decomposition of complex multi-fold phase synchronization loops, demonstrating that individual harmonic components maintain linear phase synchronization even as their synchronization gradients decrease at higher harmonic orders. Leveraging these nonlinear mechanisms, a multi-objective Genetic Algorithm (GA) is used to optimize geometric and stiffness parameters, expanding the half-power bandwidth by 218.8% without sacrificing the peak power output. Beyond energy harvesting, the proposed semi-analytical HB reconstruction and phase synchronization frameworks provide broadly applicable methodologies for characterizing strongly nonlinear coupled oscillators and advancing vibration-based structural health monitoring systems.