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The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems

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Nonlinear Dynamics, Volume 1

Abstract

Because nowadays structural engineers are willing to use or at least understand nonlinearities instead of simply avoiding them, there is a need for numerical tools performing analysis of nonlinear large-scale structures. Among these techniques, the harmonic balance (HB) method is certainly one of the most commonly used to study finite element models with reasonably complex nonlinearities. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. For this reason, the present paper proposes to extend the method to the detection and tracking of codimension-1 bifurcations in the system parameters space. As an application, the frequency response of a spacecraft is studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. This example illustrates how bifurcation tracking using the HB method can be employed as a promising design tool for detecting and eliminating such undesired behaviors.

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Acknowledgements

The authors Thibaut Detroux, Luc Masset and Gaetan Kerschen would like to acknowledge the financial support of the European Union (ERC Starting Grant NoVib 307265).

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Authors and Affiliations

  1. Space Structures and Systems Laboratory (S3L), Structural Dynamics Research Group,Department of Aerospace and Mechanical Engineering, University of Liège, Liège, Belgium

    T. Detroux, L. Renson, L. Masset & G. Kerschen

Authors
  1. T. Detroux
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  2. L. Renson
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  3. L. Masset
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  4. G. Kerschen
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Correspondence to T. Detroux .

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Editors and Affiliations

  1. Space Structures and Systems Laboratory, University of Liège, Liège, Belgium

    Gaëtan Kerschen

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© 2016 The Society for Experimental Mechanics, Inc.

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Detroux, T., Renson, L., Masset, L., Kerschen, G. (2016). The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-15221-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-15221-9_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15220-2

  • Online ISBN: 978-3-319-15221-9

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