Dynamic Analysis of Rotating Nonuniform Timoshenko Beams With an Elastically Restrained Root

[+] Author and Article Information
S. M. Lin

Mechanical Engineering Department, Kung Shan Institute of Technology, Tainan, Taiwan 710-03, R.O.C.

J. Appl. Mech 66(3), 742-749 (Sep 01, 1999) (8 pages) doi:10.1115/1.2791698 History: Received September 12, 1997; Revised January 19, 1999; Online October 25, 2007


A systematic solution procedure for studying the dynamic response of a rotating nonuniform Timoshenko beam with an elastically restrained root is presented. The partial differential equations are transformed into the ordinary differential equations by taking the Laplace transform. The two coupled governing differential equations are uncoupled 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 general solution and the generalized Green function of the uncoupled system are derived. They are expressed in terms of the four corresponding linearly independent homogenous solutions, respectively. The shifting relations of the four homogenous solutions of the uncoupled governing differential equation with constant coefficients are revealed. The generalized Green function of an nth order ordinary differential equation can be obtained by using the proposed method. Finally, the influence of the elastic root restraints, the setting angle, and the excitation frequency on the steady response of a beam is investigated.

Copyright © 1999 by The American Society of Mechanical Engineers
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