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Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods

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  • Awrejcewicz, J.
  • Krysko, V.A.
  • Papkova, I.V.
  • Krysko, A.V.

Abstract

In this work chaotic dynamics of continuous mechanical systems such as flexible plates and shallow shells is studied. Namely, a wide class of the mentioned objects is analyzed including flexible plates and cylinder-like panels of infinite length, rectangular spherical and cylindrical shells, closed cylindrical shells, axially symmetric plates, as well as spherical and conical shells. The considered problems are solved by the Bubnov–Galerkin and higher approximation Ritz methods. Convergence and validation of those methods are studied. The Cauchy problems are solved mainly by the fourth Runge-Kutta method, although all variants of the Runge-Kutta methods are considered. New scenarios of transition from regular to chaotic orbits are detected, analyzed and discussed.

Suggested Citation

  • Awrejcewicz, J. & Krysko, V.A. & Papkova, I.V. & Krysko, A.V., 2012. "Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 687-708.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:6:p:687-708
    DOI: 10.1016/j.chaos.2012.01.016
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    Cited by:

    1. Petkov, Boyan H., 2015. "Difficulties in detecting chaos in a complex system," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 35-47.
    2. Feng, Jinqian & Liu, Junli, 2015. "Chaotic dynamics of the vibro-impact system under bounded noise perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 10-16.

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