Vibration Modes and Frequencies of Timoshenko Beams With Attached Rigid Bodies

[+] Author and Article Information
M. W. D. White, G. R. Heppler

Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario N2L 2G1, Canada

J. Appl. Mech 62(1), 193-199 (Mar 01, 1995) (7 pages) doi:10.1115/1.2895902 History: Received March 04, 1993; Revised December 27, 1993; Online October 30, 2007


The equations of motion and boundary conditions for a free-free Timoshenko beam with rigid bodies attached at the endpoints are derived. The natural boundary conditions, for an end that has an attached rigid body, that include the effects of the body mass, first moment of mass, and moment of inertia are included. The frequency equation for a free-free Timoshenko beam with rigid bodies attached at its ends which includes all the effects mentioned above is presented and given in terms of the fundamental frequency equations for Timoshenko beams that have no attached rigid bodies. It is shown how any support / rigid-body condition may be easily obtained by inspection from the reported frequency equation. The mode shapes and the orthogonality condition, which include the contribution of the rigid-body masses, first moments, and moments of inertia, are also developed. Finally, the effect of the first moment of the attached rigid bodies is considered in an illustrative example.

Copyright © 1995 by The American Society of Mechanical Engineers
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