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Vibratory Energy Localization by Non-smooth Energy Sink with Time-Varying Mass

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Applied Non-Linear Dynamical Systems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 93))

Abstract

We study nonlinear interactions of two coupled oscillators at different time scales. The main oscillator which is linear is coupled to a nonlinear energy sink with non-smooth (piecewise linear) potential and time-dependent mass. The overall time is embedded to fast and slow time scales and the behavior of the system at each one of them is revealed.The invariant of the system at fast time scale is detected. Then we try to have further information about the overall system behavior at the first slow time scale. Finally, analytical developments are compared with numerical results and the possibility of the passive control of the main system by means of the time-dependent NES is commented upon.

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Acknowledgements

The authors would like to thank the following organization for supporting this research work: LABEX CELYA (ANR-10-LABX-0060) of the “Université de Lyon” within the program “Investissement d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

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Authors and Affiliations

  1. ENTPE, Université de Lyon, LGCB and LTDS UMR CNRS 5513, Rue Maurice Audin, 69518, Vaulx en Velin, France

    Alireza Ture Savadkoohi & Claude-Henri Lamarque

Authors
  1. Alireza Ture Savadkoohi
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  2. Claude-Henri Lamarque
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Corresponding author

Correspondence to Alireza Ture Savadkoohi .

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Editors and Affiliations

  1. Department of Automation, Biomechanics and Mechatronics, Łódź University of Technology, Łódź, Poland

    Jan Awrejcewicz

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Savadkoohi, A.T., Lamarque, CH. (2014). Vibratory Energy Localization by Non-smooth Energy Sink with Time-Varying Mass. In: Awrejcewicz, J. (eds) Applied Non-Linear Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 93. Springer, Cham. https://doi.org/10.1007/978-3-319-08266-0_32

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