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Localized Buckling as Statical Homoclinic Soliton and Spacial Complexity

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Nonlinear Dynamics in Engineering Systems

Summary

The work is aiming at establishing a connection between soliton, chaos and buckling of elastic structures. We discuss two evolutionary, completely integrable nonlinear differential equations with three types of localized solutions; loop soliton, cusp soliton and envelope soliton. After giving a mechanical interpretation to these equations, the first as the dynamical elastica and the second as that governing localized buckling waves in an elastic cylindrical shell, we use a blend of numerical, theoretical and experimental reasoning to show the homoclinicity of these solutions. This in turn may lead through deterministic spacial fluctuation to spacial asymptotic chaos in the sense of Roessler.

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Authors and Affiliations

  1. King Abdul Aziz City of Science and Technology, Riyadh, Kingdom of Saudi Arabia

    M. S. El Naschie & S. Al Athel

  2. Mechanical Engineering Department, University of Surrey, Guildford, UK

    A. C. Walker

Authors
  1. M. S. El Naschie
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  2. S. Al Athel
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  3. A. C. Walker
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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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El Naschie, M.S., Al Athel, S., Walker, A.C. (1990). Localized Buckling as Statical Homoclinic Soliton and Spacial Complexity. 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_9

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  • DOI: https://doi.org/10.1007/978-3-642-83578-0_9

  • 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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