REGIMES OF HARMONICALLY FORCED LINEAR OSCILLATOR WITH ATTACHED NONLINEAR ENERGY SINK NEAR THE MAIN RESONANCE

Oleg Gendelman, Yuli Starosvetsky

Dynamic responses of a linear oscillator coupled to a nonlinear energy sink (NES) under harmonic forcing in the regime of 1:1 resonance are investigated. Primary attention is paid to detailed investigation of so-called strongly modulated response (SMR), which is not related to the fixed points of average modulation equations of the system. It is demonstrated that the SMR is related to a relaxation – type motion and its description may be reduced to one – dimensional discrete mapping of a subset at a fold line of slow invariant manifold of the system.

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