Dynamics of coupled linear and essentially nonlinear oscillators with substantially different masses

The dynamics of a linear oscillator, coupled to an essentially nonlinear attachment of substantially lower mass, is investigated. The essential (nonlinearizable) nonlinearity of the attachment enables it to resonate with the oscillator, leading to energy pumping phenomena, e.g., passive, almost irreversible transfer of energy from the substructure to the attachment. Feasibility of this process for possible applications depends on relative mass of the attachment, the obvious goal being to minimize it while preserving the efficiency of the pumping. Two different models of the attachment coupled to the main single-degree-of-freedom body are proposed and analyzed both analytically and numerically. It is demonstrated that efficient energy pumping may be obtained for a rather small value of the attachment mass. Two mechanisms of energy pumping in the system under consideration are revealed. The first one is similar to previously studied resonance capture; a novel analytic framework allowing explicit account of the damping is proposed. The second mechanism is related to nonresonant excitation of high-frequency vibrations of the attachment. Both mechanisms are demonstrated numerically for a model consisting of a linear chain with a nonlinear attachment.