Multi-Scale Energy Pumping Between a Main Oscillator Including Saint-Venant Term and a Nonlinear Energy Sink

Abstract eng:
Vibratory energy exchange between oscillators can be used for localization, passive control and/or energy harvesting. It has been demonstrated, theoretically and experimentally, that by coupling an essential nonlinear and light oscillator to main oscillators, it will be possible to passively control the main system against externally induced forces. The phenomenon is called energy pumping and the nonlinear oscillator is named as nonlinear energy sink (NES). Some research works have been carried out in order to detect the energy pumping between linear and non-polynomial/nonsmooth NES systems or between a nonsmooth main oscillator and a coupled cubic NES. In this work, multi-scale vibratory energy exchange between a main oscillator including Saint-Venant term and a cubic nonlinear energy sink is studied. Analytically obtained invariant manifold of the system at fast time scale and detected fixed points and/or fold singularities at first slow time scale let us predict and explain different regimes that the system may face during the energy exchange process. The work will be accompanied by two numerical examples confirming our analytical developments.

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