Effect of the suspended block's weight on the nonlinear dynamics of a non-ideal magnetic levitation model connected to an energy harvester

Magnetic levitation (MAGLEV) technology over the years has attracted significant attention, not just for transportation purposes - as in MAGLEV trains and vehicles, but also for energy harvesting purposes. This paper presents a detailed study of a non-ideal magnetic levitation system, emphasizing the potential for energy harvesting while taking into account the weight of the oscillating suspended block in the middle. Geometry of axis translation is used to account for the new consideration of the middle block's weight. Both numerical simulations using Runge-Kutta method and analytical solution through the method of multiple scales are utilized to study the system's behavior. Numerical results confirm resonance behaviors of the middle block and electrodynamic shaker, supported by phase plane and Poincare maps describing system stability under varying conditions. Through the analytical findings, the study considers the system's response to mechanical-electrical damping variations and center magnet mass changes. Parametric variations reveal subtle effects on system dynamics, showing the relationship between damping, mass, and the oscillation amplitude. Moreover, power output analyses indicate that, at the presence of internal resonance, the power is approximately three times more than the case of absence of internal resonance. Overall, incorporating weight yields better power output, making the way for future research development in system design and application.