Harnessing energy pumping in mechanical systems: This research explores energy pumping in a damped system with essential nonlinearities, using both analytical techniques and numerical simulations. The equations of motion are transformed using action-angle variables, enabling the application of two-frequency averaging. The authors demonstrate that energy pumping occurs due to resonance capture in the 1:1 resonance manifold of the system. Perturbation analysis is performed to analyze attracting regions and understand resonance capture. The second method assumes 1:1 internal resonance in the system's fast dynamics, using complexification and averaging to develop analytical approximations to nonlinear transient responses in the energy pumping regime. Complexification and averaging are utilized to develop analytical approximations to the nonlinear transient responses of the system in the energy pumping regime. These results were found to be closely related to results collected from numerical simulations. The findings offer insights into the design of systems that can efficiently transfer and dissipate energy, with potential applications in vibration damping, energy harvesting, and nonlinear dynamics control.
Published in the Journal of Applied Mechanics, this paper aligns with the journal’s focus on mechanics and engineering applications. By analyzing energy pumping in nonlinear oscillators, the research contributes to the understanding of dynamical systems and control, with significant implications for vibration control and energy harvesting technologies. Its lasting citations by researches continues to influence the field.