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On an approximate criterion for chaotic motion in a model of a buckled beam

Ein Näherungskriterium für chaotisches Verhalten in einem Modell eines geknickten Balkens

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Summary

Periodic and chaotic motions in a mathematical model of a buckled beam are studied by the aid of approximate theory of nonlinear vibration and computer simulation. It is shown that the first approximate harmonic solution of small orbit motion may provide an approximate criterion for chaotic motion to appear. While computer simulation shows a variety of subharmonic motions (period doubling bifurcation) critical system parameters calculated on the assumption of harmonic solution prove to be close to the true boundaries of chaotic zone.

Übersicht

Periodische und chaotische Bewegungen in einem Modell des geknickten Balkens werden mit Hilfe von Näherungsverfahren der Theorie nichtlinearer Schwingungen und Computersimulationen untersucht. Es wird veranschaulicht, daß die erste harmonische Näherungslösung näherungsweise ein Kriterium für das Auftreten des chaotischen Verhaltens liefern kann. Obwohl eine Menge von subharmonischen Lösungen (Perioden-Verdopplung-Verzweigungen) bei den Simulationen festzustellen ist, scheinen die aufgrund des harmonischen Ansatzes berechneten kritischen Parameterwerte nahe der wirklichen Grenze des chaotischen Parameterbereiches zu liegen.

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Authors and Affiliations

  1. Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, PL-00-049, Warsaw, Poland

    J. Rudowski &  W. Szemplińska -Stupnicka

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  1. J. Rudowski
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  2. W. Szemplińska -Stupnicka
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Rudowski, J., Szemplińska -Stupnicka, W. On an approximate criterion for chaotic motion in a model of a buckled beam. Ing. arch 57, 243–255 (1987). https://doi.org/10.1007/BF02570610

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  • DOI: https://doi.org/10.1007/BF02570610

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