Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. I: Description of response regimes. (English) Zbl 1170.70332
Summary: A series of two papers is devoted to detailed investigation of the response regimes of linear oscillator with attached nonlinear energy sink (NES) under harmonic external forcing and assessment of possible application of the NES for vibration absorption and mitigation. The first paper of the series is devoted to analytic and numeric description of the attractors (response regimes) of the system. Analytic approach is based on averaging and multiple-scales analysis, the mass ratio being used as the small parameter. The problem of possible coexistence of different attractors is reduced to analysis of flow on slow invariant manifolds (SIM) of the system. Numeric simulation confirms the predictions of the analytic model concerning the number, the shape, and the structure of the response regimes and reveals some other features of these attractors.
Keywords:
attractors of forced nonlinear system; nonlinear energy sink; invariant manifolds; nonlinear normal modesReferences:
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