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Nonlinear Normal Modes of Nonconservative Systems

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Topics in Nonlinear Dynamics, Volume 1

Part of the book series: Conference Proceedings of the Society for Experimental Mechanics Series ((CPSEMS,volume 35))

Abstract

Linear modal analysis is a mature tool enjoying various applications ranging from bridges to satellites. Nevertheless, modal analysis fails in the presence of nonlinear dynamical phenomena and the development of a practical nonlinear analog of modal analysis is a current research topic. Recently, numerical techniques (e.g., harmonic balance, continuation of periodic solutions) were developed for the computation of nonlinear normal modes (NNMs). Because these methods are limited to conservative systems, the present study targets the computation of NNMs for nonconservative systems. Their definition as invariant manifolds in phase space is considered. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry.

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Acknowledgements

The author L. Renson would like to acknowledge the Belgian National Fund for Scientific Research (FRIA fellowship) for its financial support.

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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 Lige, Liege, Belgium

    L. Renson & G. Kerschen

Authors
  1. L. Renson
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  2. G. Kerschen
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Corresponding author

Correspondence to L. Renson .

Editor information

Editors and Affiliations

  1. University of Liege, Place du 20-Août 7, Liege, 4000, Belgium

    Gaetan Kerschen

  2. , School of Mechanical Engineering, Purdue University, Purdue Mall 585, West Lafayette, 47907-2088, USA

    Douglas Adams

  3. LMS International, Brussels, Belgium

    Alex Carrella

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Renson, L., Kerschen, G. (2013). Nonlinear Normal Modes of Nonconservative Systems. In: Kerschen, G., Adams, D., Carrella, A. (eds) Topics in Nonlinear Dynamics, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6570-6_17

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  • DOI: https://doi.org/10.1007/978-1-4614-6570-6_17

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6569-0

  • Online ISBN: 978-1-4614-6570-6

  • eBook Packages: EngineeringEngineering (R0)

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