• Journal of the Korean Society for Precision Engineering
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• v.26 no.9
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• pp.112-120
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• 2009

In this paper the purpose is to investigate the stability and variation of natural frequency of a cracked Timoshenko cantilever beams subjected to subtangential follower force. In addition, an analysis of the stability of a cantilever beam as the crack effect and slenderness ratio is investigated. 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. By using the results of this paper, we can obtain the judgment base that the choice of beam models for the effect of slenderness ratio and crack.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.903-906
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• 2005

The purpose of this paper is to investigate free vibrations and critical loads of the uniform Beck's columns with a tip spring, carrying a tip mass. The ordinary differential equation governing free vibrations of such Beck's column subjected to a follower force is derived based on the Bernoulli-Euler beam theory. Both the divergence and flutter critical loads are calculated from the load-frequency curves that are obtained by solving the differential equation numerically. The critical loads are presented in the figures as functions of various non-dimensional system parameters such as the mass moment of inertia and spring parameter.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.2
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• pp.183-187
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• 1986

An experimental method to give a tangential follower force to a cantilever beam having a concentrated tip mass by the magnetic force of the electromagnet has been described. The dynamic behaviour of the beam under this nonconservative load has been analysed by experimentally as well as by theoretically. The theoretical and experimental results on the natural frequencies and the critical force of the systems are in good agreement with each other.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.315.2-315
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• 2002

The vibrational system of this study consists of a cantilever pipe conveying fluid, the moving mass upon it and an attached tip mass. The equation of motion is derived by using Lagrange equation. The influences of the velocity of moving mass and the uniformly distributed tangential follower force have been studied on the dynamic behavior of a cantilever pipe by numerical method. While the moving mass moves upon the cantilever pipe, the velocity of fluid flow increase, the tip displacement of cantilever pipe conveying fluid is decreased. (omitted)

• Journal of Korean Society of Steel Construction
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• v.17 no.6 s.79
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• pp.699-705
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• 2005

This paper investigates critical loads of tapered cantilever columns with a tip mass, subjected to a follower force. The linearly tapered solid rectangular cross-sections are adopted as the column taper. The differential equation governing free vibrations of such columns, also called Beck's columns, is derived using the Bernoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves that are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters, namely, the taper type, the subtangential parameter, and the mass ratio.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.11 s.104
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• pp.1287-1294
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• 2005

The purpose of this paper is to investigate free vibrations and critical loads of the Beck's columns with a tip spring, which carry a tip mass. The ordinary differential equation governing free vibrations of Beck's column subjected to a follower force is derived based on the Bernoulli-Euler beam theory Both the divergence and flutter critical loads are calculated from the load-frequency corves that are obtained by solving the differential equation numerically. The critical loads are presented in the figures as functions of various non-dimensional system parameters such as the subtangential parameter, mass ratio and spring parameter.