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On the oscillations of statically indeterminate beams

Über die Schwingungen statisch unbestimmter Balken

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Summary

The Problem of determining the natural frequencies and modes of a statically indeterminant,Timoshenko beam is considered. By lumping the beam properties of linear and rotary inertia at discrete points along the length of the beam and by employing the complementary, variational principle, an approximate solution is obtained by simple matrix iteration.

Zusammenfassung

Das Problem der Bestimmung von Eigenfrequenzen und Schwingungsformen eines statisch unbestimmtenTimoshenkoträgers wird behandelt. Durch Zusammenziehung der Trägereigenschaften von Masse und Drehmasse an diskreten Punkten entlang des Trägers und durch Anwendung des komplementären Variationsprinzips wird eine Näherungslösung durch einfache Matrizeniteration erreicht.

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References

  1. Karnopp, B. H. andJ. C. Fung: On the approximate determination of natural frequencies and modes of cantilever beams. Acta Mech., IX, 109 (1970).

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  2. Huang, T. C.: Eigenvalues and modifying quotients of vibrations of beams. Univ. of Wis. Eng'g. Exp. Station Report No.25, 1964.

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Authors and Affiliations

  1. Department of Engineering Mechanics College of Engineering, University of Michigan, 48104, Ann Arbor, Mich., USA

    B. H. Karnopp

  2. Toronto, Canada

    B. Nagendra

Authors
  1. B. H. Karnopp
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  2. B. Nagendra
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Karnopp, B.H., Nagendra, B. On the oscillations of statically indeterminate beams. Acta Mechanica 9, 121–129 (1970). https://doi.org/10.1007/BF01176614

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  • DOI: https://doi.org/10.1007/BF01176614

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