Energy pumping in nonlinear mechanical oscillators: Part II - Resonance capture

We study energy pumping in an impulsively excited, two-degrees-of-freedom d amped system with essential (nonlinearizable) nonlinearities by means of tw o analytical techniques. First, we transform the equations of motion using the action-angle variables of the underlying Hamiltonian system and bring t hem into the form where two-frequency averaging cart be applied. We then sh ow that energy pumping is due to resonance capture in the 1:1 resonance man ifold of the system, and perform a perturbation analysis in an O (root epsi lon) neighborhood of this manifold in order to study the attracting region responsible for the resonance capture. The second method is based on the as sumption of 1:1 internal resonance in the fast dynamics of the system, and utilizes complexification and averaging to develop analytical approximation s to the nonlinear transient responses of the system in the energy pumping regime. The results compare favorably to numerical simulations. The practic al implications of the energy pumping phenomenon are discussed.