• Proceedings of the KSME Conference
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• 2008.11a
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• pp.961-966
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• 2008

In this paper, the purpose is to investigate the stability and variation of natural frequency of a Timoshenko cantilever beam subjected to Subtangential follower force and tip mass. In addition, an analysis of the flutter instability(flutter critical follower force) of a cantilever beam as slenderness ratio is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force is 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 and tip mass on the critical follower force and the natural frequency of a Timoshenko beam are investigated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.6_spc
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• pp.635-643
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• 2016

A stability theory of a damped cantilever column under sub-tangential follower forces is first summarized based on the stability map. It is then demonstrated that internal and external damping can be exactly transformed to Rayleigh damping so that the damping coefficients can be effectively determined using proportional damping. Particularly a parametric study with variation of damping coefficients is performed in association with flutter loads of Beck's column and it is shown that two damping coefficients can be correctly estimated for real systems under the assumption of Rayleigh damping. Finally a frequency equation of a cantilever beam subjected to both a sub-tangentially follower force and two kinds of damping forces is presented in the closed-form and its stability maps are constructed and compared with FE solutions in the practical range of damping coefficients.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.1
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• pp.29-38
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• 2013

This paper deals with geometrical non-linear analyses of the tapered cantilever column subjected to the sub-tangential follower force at the free end. Cross-sections of the column whose flexural rigidities are functionally varied with the axial coordinate. The differential equations governing the elastica of such column are derived on the basis of the large deformation theory. These differential equations have three unknown parameters of the vertical and horizontal deflections and rotation at the free end. These differential equations are numerically solved by the iteration technique for obtaining three unknowns and elastica of the deformed column. For validating theories developed herein, laboratory scaled experiments are conducted.