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Analysis of the Beating States in the System of Nonlinearly Coupled Parametrically Forced Oscillators

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Problems of Nonlinear Mechanics and Physics of Materials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 94))

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Abstract

Present study focuses on the special response regimes of resonant energy transfer emerging in the system of two nonlinearly coupled, parametrically forced oscillators. Assuming the 1:1 internal resonant interaction we find the special conditions on the system parameters leading to the formation of these special dynamical states in the un-damped as well as the weakly damped cases. Numerical simulation of the model under consideration is in a complete agreement with the analytical predictions derived in the study.

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Acknowledgements

Authors are grateful to Prof. L.I. Manevitch and Dr. M. Kovaleva from N.N. Semenov Institute of Chemical Physics, Moscow, Russia, for fruitful discussions.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Technion Israel Institute of Technology, 32000, Technion City, Haifa, Israel

    V. Kislovsky & Y. Starosvetsky

Authors
  1. V. Kislovsky
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  2. Y. Starosvetsky
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Corresponding author

Correspondence to Y. Starosvetsky .

Editor information

Editors and Affiliations

  1. Institut für Allgemeine Mechanik, RWTH Aachen University, Aachen, Germany

    Igor V. Andrianov

  2. Department of Theoretical and Computational Mechanics, Dnepropetrovsk National University, Dnipro, Ukraine

    Arkadiy I. Manevich

  3. Department of Applied Mathematics, National Technical University, Kharkov, Ukraine

    Yuri V. Mikhlin

  4. Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa, Israel

    Oleg V. Gendelman

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Kislovsky, V., Starosvetsky, Y. (2019). Analysis of the Beating States in the System of Nonlinearly Coupled Parametrically Forced Oscillators. In: Andrianov, I., Manevich, A., Mikhlin, Y., Gendelman, O. (eds) Problems of Nonlinear Mechanics and Physics of Materials. Advanced Structured Materials, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-319-92234-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-92234-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92233-1

  • Online ISBN: 978-3-319-92234-8

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