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Bifurcations in a Hard Spring Duffing Oscillator

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Nonlinear Dynamics in Engineering Systems

Summary

Tangent and period-doubling bifurcation curves of a hard spring Duffing oscillator are calculated with the shooting method and the continuation technique. From these curves, one observes clearly the route via period-doubling to chaos and the coexistence of multiple solutions. The results are compared with those obtained using harmonic balance method and numerical simulations.

On leave from Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200 030, PR China

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References

  1. Ling, F.H.: A numerical study of the distribution of different attractors in the parameter space Z. Phys. B—Condensed Matter to appear.

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  2. Thompson, J.M.T.: Chaotic phenomena triggering the escape from a potential well. Proc. R. Soc. Loud. A 421 (1989) 195–225.

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  3. Fang, T. and Dowell E.H.: Numerical simulations of periodic and diaotic responses in a stable Duffing system. Int. J. Non-Linear Mechanics 22 (1982) 401–425.

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  4. Ling, F.H.: Numerische Berechnung erllger nidnthnearen Schwingungssysteme. Dissertation Universität Stuttgart, 1981.

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  5. Schmidt, G. and Tonde, A.: Non-Linear Vibrations. Cambridge: Cambridge University Press 198G.

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Author information

Authors and Affiliations

  1. Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, NJ, 07030, USA

    F. H. Ling & Y. M. Cheung

Authors
  1. F. H. Ling
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  2. Y. M. Cheung
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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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Ling, F.H., Cheung, Y.M. (1990). Bifurcations in a Hard Spring Duffing Oscillator. 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_44

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  • DOI: https://doi.org/10.1007/978-3-642-83578-0_44

  • 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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