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A Stability Study of Continuous Systems under Parametric Excitation via Liapunov’s Direct Method

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Instability of Continuous Systems

Abstract

Continuous systems under parametric excitation are governed by partial differential equations with time dependent coefficients, [1]. In this paper the stability of certain systems of this type is investigated. Here the direct method of Liapunov, [2], is used. The analysis follows in spirit the work of Kozin [3], Caughey and Gray [4], and Infante [5] on dynamical systems with finite degrees of freedom subjected to random excitation, and that of Wang [6] on continuous systems. Our interest is, however, on deterministic systems. A key innovation here is believed to be the use of time dependent Liapunov functionals to obtain frequency dependent criteria.

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References

  1. Bolotin, V. V.: The Dynamic Stability of Elastic Systems, San Francisco: Holden-Day 1964.

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  2. Zubov, V. I.: Method of A. M. Lyapunov and their Application, Leningrad 1957; English translation, Groningen: P. Noordhoff 1964.

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  3. Kozin, F.: J. Math, and Phys. 42, 59 (1963).

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  4. Caughey, T. K., Gray, A. H., Jr.: J. Appl. Mech. 32, 365 (1965).

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  5. Infante, E. F.: J. Appl. Mech. 35, 7 (1968).

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  6. Wang, P. K. C.: J. Appl. Mech. 33, 182 (1966).

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  7. Infante, E. F., Plaut, R. H.: AIAA J. 7, 766 (1969).

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Author information

Authors and Affiliations

  1. University of California, Berkeley, Cal., USA

    C. S. Hsu

  2. University of California, Berkeley, Cal., USA

    T. H. Lee

  3. Lockheed Aircraft Corp., Burbank, Cal., USA

    T. H. Lee

Authors
  1. C. S. Hsu
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  2. T. H. Lee
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Editor information

Editors and Affiliations

  1. Solid Mechanics Division, Faculty of Engineering, University of Waterloo, Waterloo, Ontario, Canada

    Horst Leipholz

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© 1971 Springer-Verlag, Berlin/Heidelberg

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Hsu, C.S., Lee, T.H. (1971). A Stability Study of Continuous Systems under Parametric Excitation via Liapunov’s Direct Method. In: Leipholz, H. (eds) Instability of Continuous Systems. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65073-4_16

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  • DOI: https://doi.org/10.1007/978-3-642-65073-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-65075-8

  • Online ISBN: 978-3-642-65073-4

  • eBook Packages: Springer Book Archive

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