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Vibrations and transient responses of Timoshenko beams resting on elastic foundations

Eigenschwingungen und transientes Verhalten von Timoshenko-Balken mit elastischer Bettung

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Summary

A finite element technique is used to obtain the natural frequencies and transient responses of Timoshenko beams resting on elastic foundations. The beam is discretized into beam elements, each with four degrees of freedom. The equations of motion in terms of the nodal degrees of freedom are derived by applying Hamilton's principle. The numerical results for a hinged-hinged beam are given to show the effects of rotatory inertia, shear deformation and foundation constants on the natural frequencies of the beam. The transient responses of beams are subsequently presented and compared with the available solutions.

Übersicht

Mit einer Finit-Element-Technik werden die Eigenfrequenzen und das transiente Verhalten von Timoshenko-Balken mit elastischer Bettung ermittelt. Der Balken wird dabei in Elemente mit je vier Freiheitsgraden diskretisiert. Die Bewegungsgleichungen werden mit Hilfe des Prinzips von Hamilton hergeleitet. Numerische Ergebnisse für einen beidseitig gelenkig gelagerten Balken zeigen den Einfluß von Drehträgheit, Schubverformung und Bettungskonstanten auf die Eigenfrequenzen. Anschließend wird das transiente Verhalten dargestellt und mit bekannten Ergebnissen verglichen.

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Authors and Affiliations

  1. Division of Engineering Mechanics Faculty of Engineering, Osaka University, Suita, 565, Osaka, Japan

    T. Yokoyama

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  1. T. Yokoyama
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Yokoyama, T. Vibrations and transient responses of Timoshenko beams resting on elastic foundations. Ing. arch 57, 81–90 (1987). https://doi.org/10.1007/BF00541382

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  • DOI: https://doi.org/10.1007/BF00541382

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