Stability of Nonconservatively Elastic Systems Using Eigenvalue Sensitivity

[+] Author and Article Information
Lien-Wen Chen

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101, Republic of China

Der-Ming Ku

Aero Industry Development Center, P.O. Box 90008-11-9, Taichung, Taiwan 40722, Republic of China

J. Vib. Acoust 116(2), 168-172 (Apr 01, 1994) (5 pages) doi:10.1115/1.2930408 History: Received April 01, 1991; Online June 17, 2008


The stability of a cantilever column, carrying a concentrated mass at the free end and resting on an elastic foundation of the Winkler-type, subjected to uniformly distributed in-plane follower forces is studied by “Timoshenko beam theory” finite elements. In order to more quickly and efficiently obtain the critical load for such a nonconservative system, a simple and cost-effective numerical technique which utilizes the eigenvalue sensitivity with respect to the follower force is introduced instead of the conventional trial-and-error technique. The high accuracy and rapid rate of convergence through the combination of the present finite element model and the solution technique are demonstrated with the numerical example given. The influence of some system parameters on the critical load is also discussed.

Copyright © 1994 by The American Society of Mechanical Engineers
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