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The dynamic stability of degenerate systems under parametric excitation

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Summary

The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

Übersicht

Es wird die parametrische Resonanz eines Systems betrachtet, dessen zwei Eigenfrequenzen gleich sind. Das gleichzeitige Auftreten von Instabilitäten erster und zweiter Art wird durch eine verallgemeinerte Störungsrechnung untersucht. Der Instabilitätsbereich läßt sich dann in erster Näherung unter Benutzung des Sturmschen Satzes über die Wurzeln eines Polynoms berechnen.

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Authors and Affiliations

  1. Dept. of Civil Engineering, Indian Institute of Science, 560012, Bangalore, India

    K. S. Jagadish

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  1. K. S. Jagadish
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Additional information

The author is indebted to Prof. Dr. E. Mettler, Universität Karlsruhe, for his useful suggestions. The author's grateful thanks are due to the German Academic Exchange Service (DAAD) for the financial support at the Institut für Mechanik, Universität Karlsruhe.

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Jagadish, K.S. The dynamic stability of degenerate systems under parametric excitation. Ing. arch 43, 240–246 (1974). https://doi.org/10.1007/BF00534006

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  • DOI: https://doi.org/10.1007/BF00534006

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