Modeling Nonlinear Beam Vibrations: A Comparison Between Classical and Data-Driven Approaches

Research output: Chapter in book/report/conference proceedingConference contributionResearchpeer review

Authors

  • Sebastian Tatzko
  • Thomas Breunung
  • Hannes Wöhler
  • Alwin Förster
  • Gleb Kleyman

External Research Organisations

  • University of Maryland
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Details

Original languageEnglish
Title of host publicationNonlinear Structures and Systems
Subtitle of host publicationProceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024
EditorsMatthew R. W. Brake, Ludovic Renson, Robert J. Kuether, Paolo Tiso
PublisherSpringer
Pages95-98
Number of pages4
ISBN (electronic)978-3-031-69409-7
ISBN (print)9783031694080
Publication statusPublished - 8 Aug 2024
Event42nd IMAC, A Conference and Exposition on Structural Dynamics, IMAC 2024 - Orlando, United States
Duration: 29 Jan 20241 Feb 2024

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (electronic)2191-5652

Abstract

Vibrating slender structures often deform considerable, which trigger nonlinear behavior. For example, when the curvature is no longer small, the equations of motion contain nonlinear terms, which are often neglected assuming small vibration amplitudes. In this chapter, we experimentally observe nonlinear vibration behavior of a slender beam under harmonic excitation. We excite the bending modes of the beam and observe the forced response for different excitation levels. The frequency response shows a softening behavior with a jump phenomenon. The nonlinearity is more pronounced in higher bending modes but is already detected in the first clamped free bending motion. The experimental results are compared with an analytical approximation using the single nonlinear mode theory. The single-mode approach is appropriate for isolated modes and predicts a softening Duffing equation as a minimal nonlinear model of geometrically nonlinear beams. Finally, we obtain the governing equations directly from the measurements utilizing data-driven techniques. The underlying nonlinear differential equation is derived using test functions and sparse identification. The identified parameters are then compared to the analytical model.

Keywords

    Cantilever beam, Data-driven modeling, Duffing oscillator, Geometric nonlinearity, System identification

ASJC Scopus subject areas

Cite this

Modeling Nonlinear Beam Vibrations: A Comparison Between Classical and Data-Driven Approaches. / Tatzko, Sebastian; Breunung, Thomas; Wöhler, Hannes et al.
Nonlinear Structures and Systems : Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024. ed. / Matthew R. W. Brake; Ludovic Renson; Robert J. Kuether; Paolo Tiso. Springer, 2024. p. 95-98 (Conference Proceedings of the Society for Experimental Mechanics Series).

Research output: Chapter in book/report/conference proceedingConference contributionResearchpeer review

Tatzko, S, Breunung, T, Wöhler, H, Förster, A & Kleyman, G 2024, Modeling Nonlinear Beam Vibrations: A Comparison Between Classical and Data-Driven Approaches. in MRW Brake, L Renson, RJ Kuether & P Tiso (eds), Nonlinear Structures and Systems : Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024. Conference Proceedings of the Society for Experimental Mechanics Series, Springer, pp. 95-98, 42nd IMAC, A Conference and Exposition on Structural Dynamics, IMAC 2024, Orlando, United States, 29 Jan 2024. https://doi.org/10.1007/978-3-031-69409-7_17
Tatzko, S., Breunung, T., Wöhler, H., Förster, A., & Kleyman, G. (2024). Modeling Nonlinear Beam Vibrations: A Comparison Between Classical and Data-Driven Approaches. In M. R. W. Brake, L. Renson, R. J. Kuether, & P. Tiso (Eds.), Nonlinear Structures and Systems : Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024 (pp. 95-98). (Conference Proceedings of the Society for Experimental Mechanics Series). Springer. https://doi.org/10.1007/978-3-031-69409-7_17
Tatzko S, Breunung T, Wöhler H, Förster A, Kleyman G. Modeling Nonlinear Beam Vibrations: A Comparison Between Classical and Data-Driven Approaches. In Brake MRW, Renson L, Kuether RJ, Tiso P, editors, Nonlinear Structures and Systems : Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024. Springer. 2024. p. 95-98. (Conference Proceedings of the Society for Experimental Mechanics Series). doi: 10.1007/978-3-031-69409-7_17
Tatzko, Sebastian ; Breunung, Thomas ; Wöhler, Hannes et al. / Modeling Nonlinear Beam Vibrations : A Comparison Between Classical and Data-Driven Approaches. Nonlinear Structures and Systems : Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024. editor / Matthew R. W. Brake ; Ludovic Renson ; Robert J. Kuether ; Paolo Tiso. Springer, 2024. pp. 95-98 (Conference Proceedings of the Society for Experimental Mechanics Series).
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