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The Torsional Vibration of Uniform Thin-Walled Beams of Open Section

Published online by Cambridge University Press:  04 July 2016

J. B. Carr
J. B. Carr*
Affiliation:
Department of Mechanical Engineering, University of Salford
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Extract

The pure torsional vibration of uniform thin-walled beams of open section, which is governed by the differential equation

has been extensively analysed by Gere He derived the exact frequency equations for beams with a variety of end conditions. However, these equations are, in most cases, highly transcendental.

This note uses an energy approach to obtain approximate frequency equations for the fixed-fixed and the fixed-simply-supported beams. A fixed end is one which allows no twist and no warping and a simply-supported end allows no twist but permits warping to take place freely. The approximating functions used are those corresponding to the exact solution of the problem if the torsional resistance caused by the St Venant system of shear stresses is zero. These functions are similar to the characteristic functions of simple beams in flexure.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 73 , Issue 704 , August 1969 , pp. 672 - 674
Copyright
Copyright © Royal Aeronautical Society 1969 

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References

1. Gere, J. M. Torsional Vibrations of Beams of Thin- walled Open Section. Journal of Applied Mechanics, Vol 21,p 381, 1954.Google Scholar
2. Young, D. and Felgar, R. P. Tables of Characteristic Functions Representing the Normal Modes of Vibration of a Beam. Bureau of Engineering Research Report 4913, University of Texas, 1949.Google Scholar