Geometric Stiffening of Timoshenko Beams

[+] Author and Article Information
D. C. D. Oguamanam

Mechanical Engineering Department, University of Waterloo, Waterloo, ON N2L 3G1, Canada

G. R. Heppler

Systems Design Engineering Department, University of Waterloo, Waterloo, ON N2L3G1, Canada

J. Appl. Mech 65(4), 923-929 (Dec 01, 1998) (7 pages) doi:10.1115/1.2791936 History: Received March 24, 1997; Revised February 10, 1998; Online October 25, 2007


The equations of motion of a prismatic isotropic Timoshenko beam with a tip mass and attached to a rotating hub are derived including the effects of centrifugal forces which appear in the equations of motion as nonlinear functions of the angular speed. The Rayleigh-Ritz method is used to obtain approximate solutions for the cases of a prescribed torque profile and a prescribed hub angular speed profile. In the case of a constant torque input, the effect of the centrifugal forces is not observed until sufficient angular speed is reached. When the system is driven under a constant velocity, it is observed that, for a sufficiently high angular speed, the centrifugal forces reduce the vibration amplitude.

Copyright © 1998 by The American Society of Mechanical Engineers
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