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Multi-scale energy exchanges between an elasto-plastic oscillator and a light nonsmooth system with external pre-stress

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Abstract

Vibratory energy exchanges between two coupled oscillators is studied: the main elasto-plastic oscillator is coupled to a nonlinear energy sink(NES) with nonsmooth potential. Both oscillators are under pre-stressing terms. Two different methods are implemented for tracing system behaviours: (i) the time-event-driven technique which builds exact solutions of governing equations of the system phase by phase and (ii) the multi-scale method which traces system behaviours at different scales of time. It detects invariant of the system at fast timescale and equilibrium/singular points at slow timescales. The pre-stressing terms produce a more complex shape for the invariant, while detected dynamics at slow timescale let us have control at the behaviour of the system during its quasi-steady-state regime(s) which leads to have analytical design tools for tuning parameters of nonlinear energy sink according to design purposes (passive control and/or energy harvesting).

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Acknowledgments

This work is supported by: (i) The “Ministère de l’Écologie, du Développement Durable et de l’Énergie” and (ii) LABEX CELYA (ANR-10-LABX-0060) of the “Université de Lyon” within the programme “Investissement d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

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Authors and Affiliations

  1. Département Laboratoire de Bordeaux, Cerema - Direction territoriale Sud-Ouest, 24 rue carton - CS 41635, Bordeaux Cedex, 33073, France

    Mathieu Weiss & Bastien Vaurigaud

  2. Badji Mokhtar-Annaba, University of Algeria, LGC and LMGE, PO Box 12, 23000, Annaba, Algeria

    Mahmoud Chenia & Abdelaziz Hammouda

  3. École Nationale des Travaux Publics de l’État, Université de Lyon, LGCB and LTDS UMR CNRS 5513, rue Maurice Audin, Vaulx-en-Velin Cedex, 69518, France

    Mathieu Weiss, Alireza Ture Savadkoohi & Claude-Henri Lamarque

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  1. Mathieu Weiss
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  2. Mahmoud Chenia
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  3. Alireza Ture Savadkoohi
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  4. Claude-Henri Lamarque
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  5. Bastien Vaurigaud
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  6. Abdelaziz Hammouda
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Correspondence to Mathieu Weiss.

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M. Weiss and M. Chenia are joint first authors.

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Weiss, M., Chenia, M., Ture Savadkoohi, A. et al. Multi-scale energy exchanges between an elasto-plastic oscillator and a light nonsmooth system with external pre-stress. Nonlinear Dyn 83, 109–135 (2016). https://doi.org/10.1007/s11071-015-2314-8

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  • DOI: https://doi.org/10.1007/s11071-015-2314-8

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