Dynamics of linear oscillator coupled to strongly nonlinear attachment with multiple states of equilibrium

Energy transfer in 2 DOF systems comprised of linear oscillator with unit mass and strongly nonlinear oscillator with multiple states of equilibrium and relatively small mass is investigated by analytic and numerical methods. We demonstrate that the process of energy transfer is governed by structure of damped nonlinear normal modes of the system. Various dynamical regimes dependent on the system parameters are revealed and conditions for efficient energy pumping to the strongly nonlinear attachment are formulated. Possibility of transient chaotic response is investigated.