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The Approximate Criteria for Chaos in Multi-well Potential Vibrating Systems

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Nonlinear Dynamics in Engineering Systems

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Summary

Application of perturbation methods to the study of transition to/from chaotic motion and determination of the system parameter critical values are discussed. The qT-periodic motion is definied by low order approximate solution obtained by perturbation methods. Higher order instabilities are examined by considering the variational Hills type equation. The instabilities which bring a build-up of 2qT harmonic components, or even order harmonics in symmetric systems, are determined in the first or second approximation, and are identified as the approximate criteria for chaos.

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References

  1. Moon F.C.: Chaotic vibrations, New York, John Wiley and Sons, 1987.

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  2. Szemplidska-Stupnicka W.: The Refined Approximate Criterion for Chaos in a Two-State Mechanical Oscillator, Ing. Archiv 58, 1988, 354–366.

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  3. Rudowski J.: Transition from symmetric periodic oscillations to chaos in a nonlinear oscillator, Reports of I.F.T.R. 22/1988 (in polish).

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  4. Szemplidska-Stupnicka W.: Plaut R.H.; Hsieh J.C.: Period Doubling and Chaos in Unsymmetric Structures under Parametric Excitation, J,Appl.Mech. (to appear).

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  5. Szemplidska-Stupnicka W.: Transition to Chaos in the Two-Well Potential System in the ultraharmonic resonance frequency region. Journal of Sound and Vibration (to appear).

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Author information

Authors and Affiliations

  1. Institute of Fundamental Technological Research PAS, Warsaw, Poland

    W. Szemplinska-Stupnicka

Authors
  1. W. Szemplinska-Stupnicka
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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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Szemplinska-Stupnicka, W. (1990). The Approximate Criteria for Chaos in Multi-well Potential Vibrating Systems. 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_38

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  • DOI: https://doi.org/10.1007/978-3-642-83578-0_38

  • 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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