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Nonlinear Modes of Cantilever Beams at Extreme Amplitudes: Numerical Computation and Experiments

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Nonlinear Structures & Systems, Volume 1

Abstract

A novel method for the numerical computation of the nonlinear normal modes (NNMs) of a highly flexible cantilever beam is presented. The flexible cantilever is modeled using a 2D finite element discretization of the geometrically exact beam model, wherein geometric nonlinearities relating to the rotation are kept entirely intact. The model is then solved using the proposed solution method, which is fully frequency domain-based and involves a novel combination of a harmonic balance (HBM) Fourier expansion with asymptotic numerical (ANM) continuation for periodic solutions. The NNMs are also calculated experimentally using a flexible cantilever specimen mounted to a shaker table. The experimental NNMs can be compared to their numerical counterparts in order to validate the frequency domain numerical technique.

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Acknowledgments

This project is part of the THREAD European Training Network “Joint Training on Numerical Modeling of Highly Flexible Structures for Industrial Applications.” This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 860124.

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Authors and Affiliations

  1. Arts et Métiers Institute of Technology, LISPEN, HESAM Université, Lille, France

    Marielle Debeurre, Aurélien Grolet & Olivier Thomas

  2. Laboratoire de Mécanique et d’Acoustique, Ecole Centrale Marseille, Marseille, France

    Pierre-Olivier Mattei & Bruno Cochelin

Authors
  1. Marielle Debeurre
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  2. Aurélien Grolet
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  3. Pierre-Olivier Mattei
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  4. Bruno Cochelin
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  5. Olivier Thomas
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Corresponding author

Correspondence to Marielle Debeurre .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Rice University, Houston, TX, USA

    Matthew R.W. Brake

  2. Department of Mechanical Engineering, Imperial College London, London, UK

    Ludovic Renson

  3. Sandia National Laboratories, Albuquerque, NM, USA

    Robert J. Kuether

  4. Department of Mechanical and Process Engineering, ETH Zürich, Zürich, Switzerland

    Paolo Tiso

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Debeurre, M., Grolet, A., Mattei, PO., Cochelin, B., Thomas, O. (2023). Nonlinear Modes of Cantilever Beams at Extreme Amplitudes: Numerical Computation and Experiments. In: Brake, M.R., Renson, L., Kuether, R.J., Tiso, P. (eds) Nonlinear Structures & Systems, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-031-04086-3_35

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  • DOI: https://doi.org/10.1007/978-3-031-04086-3_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-04085-6

  • Online ISBN: 978-3-031-04086-3

  • eBook Packages: EngineeringEngineering (R0)

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