Bending Vibrations of Rotating Nonuniform Timoshenko Beams With an Elastically Restrained Root

[+] Author and Article Information
Sen Yung Lee

Mechanical Engineering Department, National Cheng Kung University, Tainan, Taiwan 701, R.O.C.

Shueei Muh Lin

Mechanical Engineering Department, Kung Shan Institute of Technology, Tainan, Taiwan 710, R.O.C.

J. Appl. Mech 61(4), 949-955 (Dec 01, 1994) (7 pages) doi:10.1115/1.2901584 History: Received February 01, 1993; Revised November 05, 1993; Online March 31, 2008


Without considering the Coriolis force, the governing differential equations for the pure bending vibrations of a rotating nonuniform Timoshenko beam are derived. The two coupled differential equations are reduced into two complete fourth-order differential equations with variable coefficients in the flexural displacement and in the angle of rotation due to bending, respectively. The explicit relation between the flexural displacement and the angle of rotation due to bending is established. The frequency equations of the beam with a general elastically restrained root are derived and expressed in terms of the four normalized fundamental solutions of the associated governing differential equations. Consequently, if the geometric and material properties of the beam are in polynomial forms, then the exact solution for the problem can be obtained. Finally, the limiting cases are examined. The influence of the coupling effect of the rotating speed and the mass moment of inertia, the setting angle, the rotating speed and taper ratio on the natural frequencies, and the phenomenon of divergence instability (tension buckling) are investigated.

Copyright © 1994 by The American Society of Mechanical Engineers
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