RESEARCH PAPERS: System Response

On a Finite Element Formulation of Dynamical Torsion of Beams Including Warping Inertia and Shear Deformation Due to Nonuniform Warping

[+] Author and Article Information
A. Potiron, D. Gay

Department of Mechanics, I.N.S.A., 31077 Toulouse, France

J. Vib., Acoust., Stress, and Reliab 105(4), 476-483 (Oct 01, 1983) (8 pages) doi:10.1115/1.3269131 History: Received June 24, 1981; Online November 23, 2009


We start from the energetical expressions of dynamical torsion of beams in terms of angular and warping displacement and velocity. We derive the stiffness and two mass matrices including both secondary effects for torsion: the shear deformation due to nonuniform warping and the warping inertia. The suitability of these matrices for evaluation modified torsional frequencies is investigated in the case of thick, as well as thin-walled, cross section beams by comparison with analytical and experimental results.

Copyright © 1983 by ASME
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