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Energy Transfers in a System of Two Coupled Oscillators with Essential Nonlinearity: 1:1 Resonance Manifold and Transient Bridging Orbits

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Abstract

The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed.

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Authors and Affiliations

  1. Department of Materials, Mechanical and Aerospace Engineering, University of Liège, Belgium

    Gaetan Kerschen

  2. Division of Mechanics, National Technical University of Athens, USA

    Alexander F. Vakakis

  3. Department of Mechanical and Industrial Engineering (adjunct), University of Illinois at Urbana-Champaign, USA

    Alexander F. Vakakis

  4. Department of Aerospace Engineering (adjunct), University of Illinois at Urbana-Champaign, USA

    Alexander F. Vakakis

  5. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, USA

    Gaetan Kerschen & Young S. Lee

  6. Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, USA

    D. Michael Mcfarland, Jeffrey J. Kowtko & Lawrence A. Bergman

Authors
  1. Gaetan Kerschen
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  2. Alexander F. Vakakis
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  3. Young S. Lee
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  4. D. Michael Mcfarland
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  5. Jeffrey J. Kowtko
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  6. Lawrence A. Bergman
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Corresponding author

Correspondence to Gaetan Kerschen.

Additional information

This study was carried out while the author was a postdoctoral fellow at the National Technical University of Athens and at the University of Illinois at Urbana-Champaign.

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Kerschen, G., Vakakis, A.F., Lee, Y.S. et al. Energy Transfers in a System of Two Coupled Oscillators with Essential Nonlinearity: 1:1 Resonance Manifold and Transient Bridging Orbits. Nonlinear Dyn 42, 283–303 (2005). https://doi.org/10.1007/s11071-005-4475-3

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  • DOI: https://doi.org/10.1007/s11071-005-4475-3

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