Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads

[+] Author and Article Information
S. H. Choi, C. Pierre, A. G. Ulsoy

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125

J. Vib. Acoust 114(2), 249-259 (Apr 01, 1992) (11 pages) doi:10.1115/1.2930255 History: Received November 01, 1990; Online June 17, 2008


The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.

Copyright © 1992 by The American Society of Mechanical Engineers
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