Dynamic Behavior of Cracked Timoshenko Beams Subjected to Sub-tangential Follower Force

• Published in: Journal of Power System Engineering Vol. 24; no. 4; pp. 60 - 67
• Main Author: Son, In-Soo
• Format: Journal Article
• Language: English
• Published: 한국동력기계공학회 31.08.2020
• Subjects: 기타공학; Cracked Timoshenko beam; Slenderness ratio; Stability; Sub-tangential follower force; Tip mass
• ISSN: 2713-8429; 1226-7813; 2713-8437; 2384-1354
• DOI: 10.9726/kspse.2020.24.4.060

In this paper, the purpose is to investigate the stability and variation of the natural frequency of a cracked Timoshenko cantilever beam subjected to sub-tangential follower force and a tip mass. In addition, an analysis of the flutter instability of a cantilever beam according to the change of slenderness ratio is studied. The governing differential equations of a Timoshenko beam, subjected to an end tangential follower force, are derived via Hamilton’s principle. The two coupled governing differential equations are reduced to one-fourth order ordinary differential equation in terms of the flexural displacement. Finally, the influence of the slenderness ratio, a tip mass on the critical follower force, and the natural frequency of a Timoshenko beam are investigated. It is found that a difference of only 29% between the first natural frequency of the Euler beam model and that of the Timoshenko beam exists in the special case. By using the results of this paper, a judgment base is obtained as regards the choice of cracked beam models for the effect of the slenderness ratio and sub-tangential follower force. Furthermore, the effect of crack on the dynamic behavior of beams with a tip mass is investigated. KCI Citation Count: 0