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Effect of Constant Transverse Force on Chaotic Oscillations of Sinusoidally Excited Buckled Beam

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Nonlinear Dynamics in Engineering Systems

Summary

The chaotic oscillation of a buckled beam under sinusoidally varying and static constant transverse external forces is investigated. A harmonic balance method and a direct numerical integration are applied to a Duffings equation model of the buckled beam. For a small transverse constant force, there exist three static equilibrium points, and the near contact between the two orbits of a stable and an unstable limit cycle in the phase plane can predict the onset of chaos. For a large transverse constant force, there exists only one static equilibrium point, but there may exist three different dynamic response amplitudes due to nonlinear resonance phenomena. The near contact between two vibration regions of a stable and an unstable limit cycle can predict the onset of chaos.

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References

  1. Moon, F.: Experiments on Chaotic Motions of a Forced Nonlinear Oscillator: Strange Attractors. J.Appl.Mech., 47, (1980), 638–644.

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  4. Von Dooren, R.: On the Transition From Regular To Chaotic Behavior in the Duffing Oscillator. J.Sound Vib., 123 (2), (1988), 327–339.

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Author information

Author notes

  1. K. Higuchi

    Present address: Tokyo Denki University, Hatoyama, Saitama, 350-03, Japan

Authors and Affiliations

  1. Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, 27706, USA

    K. Higuchi & E. H. Dowell

Authors
  1. K. Higuchi
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  2. E. H. Dowell
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Editor information

Editors and Affiliations

  1. Institute B of Mechanics, University of Stuttgart, Pfaffenwaldring 9, D-7000, Stuttgart 80, Germany

    W. Schiehlen

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© 1990 Springer-Verlag Berlin Heidelberg

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Higuchi, K., Dowell, E.H. (1990). Effect of Constant Transverse Force on Chaotic Oscillations of Sinusoidally Excited Buckled Beam. In: Schiehlen, W. (eds) Nonlinear Dynamics in Engineering Systems. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83578-0_13

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  • DOI: https://doi.org/10.1007/978-3-642-83578-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83580-3

  • Online ISBN: 978-3-642-83578-0

  • eBook Packages: Springer Book Archive

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