Isolated resonance captures and resonance capture cascades leading to single- or multi-mode passive energy pumping in damped coupled oscillators

We examine passive energy pumping in a system of damped coupled oscillators. This is a one-way, passive and irreversible energy flow from a linear main system to a nonlinear attachment that acts, in essence, as a nonlinear energy sink (NES). Energy pumping is caused by 1:1 resonance captures on resonant manifolds of the damped systems. We show that the NES is capable of absorbing significant portions of the energies generated by transient, broadband external excitations. By performing a series of numerical simulations we confirm that the energy dependence of the nonlinear normal modes (NNMs) of the underlying undamped, unforced system determines, in essence, the resonance capture and energy pumping dynamics in the corresponding damped system. We present numerical simulations of single- and multi-mode energy pumping, that involve isolated resonance captures or resonance capture cascades, respectively. In addition, we discuss methodologies for enhancing the nonlinear energy pumping phenomenon by properly selecting the system parameters. The described technique of passively localizing and locally eliminating externally induced energy provides a new paradigm for vibration and shock isolation of mechanical oscillators.