Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

[+] Author and Article Information
Jean Wu-Zheng Zu, Ray P. S. Han

Department of Mechanical Engineering, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada

J. Appl. Mech 59(2S), S197-S204 (Jun 01, 1992) doi:10.1115/1.2899488 History: Received September 27, 1990; Revised April 30, 1991; Online March 31, 2008


A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

Copyright © 1992 by The American Society of Mechanical Engineers
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