Dynamic stiffness for piecewise non-uniform Timoshenko column by power series—part II: Follower force

✍ Scribed by A. Y. T. Leung; W. E. Zhou; C. W. Lim; R. K. K. Yuen; U. Lee

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 276 KB
• Volume: 51
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.153

✦ Synopsis

Abstract

A follower force is an applied force whose direction changes according to the deformed shape during the course of deformation. The dynamic stiffness matrix of a non‐uniform Timoshenko column under follower force is formed by the power‐series method. The dynamic stiffness matrix is unsymmetrical due to the non‐conservative nature of the follower force. The frequency‐dependent mass matrix is still symmetrical and positive definite according to the extended Leung theorem. An arc length continuation method is introduced to find the influence of a concentrated follower force, distributed follower force, end mass and stiffness, slenderness, and taper ratio on the natural frequency and stability. It is found that the power‐series method can handle a very wide class of dynamic stiffness problem. Copyright © 2001 John Wiley & Sons, Ltd.