Passive vibration control by nonlinear energy pumping: Theoretical and experimental results

We analyze energy pumping phenomena in a linear periodic substructure, weakly coupled to an essentially nonlinear attachment. By energy pumping we denote passive, one-way, irreversible transfer of energy from the linear substructure to the nonlinear attachment. As a specific application the dynamics of a system of linear coupled oscillators with a nonlinear end attachment is examined. Both theoretical and experimental results are discussed, including resonance capture cascades, i.e., a series of energy pumping phenomena occurring at different frequencies, with sudden lower frequency transitions between sequential events. The observed multifrequency energy pumping cascades are particularly interesting from a practical point of view, since they indicate that nonlinear attachments can be designed to resonate and extract energy from an a priori specified set of modes of a linear structure, in compatibility with the design objectives.