Energy pumping in nonlinear mechanical oscillators: Part I - Dynamics of the underlying Hamiltonian systems

The systems considered in this work are composed of weakly coupled, linear and essentially nonlinear (nonlinearizable) components. In part I of this w ork we present numerical evidence of energy pumping in coupled nonlinear me chanical oscillators, i.e., of one-way (irreversible) ''channeling'' of ext ernally imparted energy from the linear to the nonlinear part of the system , provided that the energy is above a critical level. Clearly no such pheno menon is possible in the linear system. To obtain a better understanding of the energy pumping phenomenon we first analyze the dynamics of the underly ing Hamiltonian system (corresponding to zero damping). First we reduce the equations of motion on an isoenergetic manifold of the dynamical flow, and then compute subharmonic orbits by employing nonsmooth transformation of c oordinates which lead to nonlinear boundary value problems. It is conjectur ed that a 1:1 stable subharmonic orbit of the underlying Hamiltonian system is mainly responsible for the energy pumping phenomenon. This orbit cannot be excited at sufficiently low energies. In Part II of this work the energ y pumping phenomenon is further analyzed, and it is shown that it is caused by transient resonance capture on a 1:1 resonance manifold of the system.