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RESEARCH PAPERS

Three-Dimensional Harmonic Vibrations of a Circular Beam

[+] Author and Article Information
D. E. Panayotounakos

The National Technical University of Athens, 5, K. Zographou Street, Zographou, Athens 624, Greece

P. S. Theocaris

Laboratory for Testing Materials, The National Technical University of Athens, 5, K. Zographou Street, Zographou, Athens 624, Greece

J. Appl. Mech 51(2), 375-382 (Jun 01, 1984) (8 pages) doi:10.1115/1.3167628 History: Received January 01, 1982; Revised June 01, 1983; Online July 21, 2009

Abstract

In this paper an analytical treatment for the determination of the natural frequencies of a circular uniform beam, subjected to three-dimensional harmonic loads, is presented. Each differential element of the beam has six degrees of freedom, i.e., three translations and three rotations. This problem, in the most general case of response, is associated with a partial linear differential system composed of four coupled 3 × 1 vectorial equations. The influences of transverse shear deformation and rotatory inertia are also included in the analysis. The aforementioned solution methodology is successfully demonstrated through several numerical results.

Copyright © 1984 by ASME
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