Abstract
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.
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Gendelman, O.V.: Transition of energy to nonlinear localized mode in highly asymmetric system of nonlinear oscillators. Nonlinear Dyn. 25, 237–253 (2001)
Gendelman, O.V., Vakakis, A.F., Manevitch, L.I., McCloskey, R.: Energy pumping in nonlinear mechanical oscillators I: Dynamics of the underlying Hamiltonian system. J. Appl. Mech. 68(1), 34–41 (2001)
Vakakis, A.F., Gendelman, O.V.: Energy pumping in nonlinear mechanical oscillators II: Resonance capture. J. Appl. Mech. 68(1), 42–48 (2001)
Lee, Y.S., Kerchen, G., Vakakis, A.F., Panagopulos, P., Bergman, L.A., McFarland, D.M.: Complicated dynamics of a linear oscillator with an essentially nonlinear local attachment. Physica D 204, 41–69 (2005)
Vakakis, A.F.: Inducing passive nonlinear energy sinks in linear vibrating systems. J. Vib. Acoust. 123(3), 324–332 (2001)
Vakakis, A.F., Manevitch, L.I., Gendelman, O., Bergman, L.: Dynamics of linear discrete systems connected to local essentially nonlinear attachments. J. Sound Vib. 264, 559–577 (2003)
Gendelman, O.V.: Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment. Nonlinear Dyn. 37(2), 115–128 (2004)
Shaw, S.W., Pierre, C.: Normal modes for nonlinear vibratory systems. J. Sound Vib. 164, 85–124 (1993)
Vakakis, A.F., Manevitch, L.I., Mikhlin, Yu.V., Pilipchuk, V.N., Zevin, A.A.: Normal Modes and Localization in Nonlinear Systems, Wiley Interscience, New York(1996)
Jang Xiaoai, McFarland, M., Bergman, L.A., Vakakis, A.F.: Steady state passive nonlinear energy pumping in coupled oscillators: Theoretical and experimental results. Nonlinear Dyn. 33, 7–102 (2003)
Gendelman, O.V., Gourdon, E., Lamarque, C.H.: Quasiperiodic energy pumping in coupled oscillators under periodic forcing. J. Sound Vib. 294, 651–662 (2006)
Gendelman, O.V., Starosvetsky, Y.: Quasiperiodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing. J. Appl. Mech., in press (2006)
Starosvetsky, Y. Gendelman, O.V.: Attractors of harmonically forced linear oscillator with attached nonlinear energy sink II: Optimization of Strongly Nonlinear Vibration Absorber, this issue (2006)
Guckenheimer, J., Hoffman, K., Weckesser, W.: Bifurcations of relaxation oscillations near folded saddles. Int. J. Bifurcation Chaos 15(11), 3411–3421 (2005)
Feldman, M.: Time-varying vibration decomposition and analysis based on the Hilbert transform. J. Sound Vib. 295, 518–530 (2006)
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Gendelman, O.V., Starosvetsky, Y. & Feldman, M. Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: Description of response regimes. Nonlinear Dyn 51, 31–46 (2008). https://doi.org/10.1007/s11071-006-9167-0
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DOI: https://doi.org/10.1007/s11071-006-9167-0