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Experimental investigation and analytical description of a vibro-impact NES coupled to a single-degree-of-freedom linear oscillator harmonically forced

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Abstract

In this paper, the dynamics of a system composed of a harmonically forced single-degree-of-freedom linear oscillator coupled to a vibro-impact nonlinear energy sink (VI-NES) is experimentally investigated. The mass ratio between the VI-NES and the primary system is about \(1\%\). Depending on the external force’s amplitude and frequency, either a strongly modulated response (SMR) or a constant amplitude response (CAR) is observed. In both cases, an irreversible transfer of energy occurs from the linear oscillator toward the VI-NES: process known in the literature as passive targeted energy transfer. Furthermore, the problem is analytically studied by using the method of multiple scales. The obtained slow invariant manifold shows the existence of a stable and of an unstable branch of solutions, as well as of an energy threshold (a saddle-node bifurcation) for the solutions to appear. Subsequently, the fixed points of the problem are calculated. When a stable fixed point is reached, the system is naturally drawn to it and a CAR is established, whereas when no stable point is attained, the system exhibits a SMR regime. Finally, a good correlation between the experimental and the analytical results is presented.

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Notes

  1. The symbol \(:=\) meaning equals by definition

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Authors and Affiliations

  1. ONERA The French Aerospace Lab, Université de Toulouse, ICA, ISAE, 92320, Châtillon, France

    Giuseppe Pennisi

  2. ONERA The French Aerospace Lab, 92320, Châtillon, France

    Cyrille Stephan

  3. Université de Toulouse, ICA, INSA, 31077, Toulouse, France

    Etienne Gourc

  4. Université de Toulouse, ICA, ISAE, 31055, Toulouse, France

    Guilhem Michon

Authors
  1. Giuseppe Pennisi
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  2. Cyrille Stephan
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  3. Etienne Gourc
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  4. Guilhem Michon
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Correspondence to Giuseppe Pennisi.

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Pennisi, G., Stephan, C., Gourc, E. et al. Experimental investigation and analytical description of a vibro-impact NES coupled to a single-degree-of-freedom linear oscillator harmonically forced. Nonlinear Dyn 88, 1769–1784 (2017). https://doi.org/10.1007/s11071-017-3344-1

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  • DOI: https://doi.org/10.1007/s11071-017-3344-1

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