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Stability of elastic rods via Liapunov's second method

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Summary

Stability of elastic rods subjected to nonconservative tangential follower forces is rigorously investigated by means of Liapunov's Second Method in the version of Movchan, Knops, and Wilkes, i.e., adapted to the specific nature of continuous systems. The result is that for such, rods internal viscous damping should have a sufficiently large magnitude in order to ensure stability. This is in agreement with, the well known fact that small damping destabilizes in the presence of nonconservative forces.

Übersicht

In dieser Arbeit wird die Stabilität elastischer Stäbe, welche nichtkonservativen tangential mitgehenden Lasten ausgesetzt sind, in strenger Weise mit Hilfe von Liapunov's Zweiter Methode untersucht, so wie diese für die Anwendung auf Kontinuierliche Systeme speziell von Movchan, Knops und Wilkes aufbereitet worden ist. Das Ergebnis ist, daß für solche Stäbe die innere, viskose Dämpfung einen genügend großen Betrag haben sollte, um Stabilität sicherzustellen. Das ist in Übereinstimmung mit der wohlbekannten Tatsache, daß geringe Dämpfung in Gegenwart von nichtkonservativen Kräften destabilisierend wirkt.

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References

  1. Leipholz, H.: Application of Liapunov's Direct Method to the Stability Problem of Rods Subject to Follower Forces. In “Instability of Continuous Systems”, Proceedings of the IUTAM Symposium Herrenalb, 1969, Berlin, Heidelberg, New York, 1971, pp. 1–10

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Authors and Affiliations

  1. Department of Civil Engineering Solid Mechanics Division, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    H. H. E. Leipholz

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  1. H. H. E. Leipholz
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Leipholz, H.H.E. Stability of elastic rods via Liapunov's second method. Ing. arch 44, 21–26 (1975). https://doi.org/10.1007/BF00534793

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  • DOI: https://doi.org/10.1007/BF00534793

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