• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.1 s.71
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• pp.85-92
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• 2006

This paper investigates critical loads of the tapered Beck's columns with clamped and spring supports, subjected to a subtangential follower force. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck's columns is derived using the Bemoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter and the spring stiffness.

• 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.

• 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 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.9
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• pp.1385-1391
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• 1997

An analysis is presented on the stability of an elastic cantilever column subjected to a concentrated follower force as to the influence of the elastic restraint and a tip mass at the free end. The elastic restraint is formed by the rotatory springs. For this purpose, the governing equations and boundary conditions are derived by using Hamilton's principle, and the critical flutter loads and frequencies are obtained from the numerical evaluation of the eigenvalue functions of the considered system.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.6 s.46
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• pp.1-12
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• 2005

For a shear-deformable beam-column element subjected io non-conservative forces, equations of motion and a finite element formulation are presented applying extended Hamilton's principle. The influence of non-conservative force's direction parameter, internal and external damping forces, and shear deformation and rotary inertia effects on divergence and flutter loads of Beck's columns are intensively investigated based on element stiffness, damping and mass matrixes derived for the non-conservative system.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.949-954
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• 2006

The purpose of this paper is to investigate the stability of tapered columns with clamped one end and carrying a tip mass of rotatory inertia with translational elastic support at the other end. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck columns is derived using the Bernoulli-Euler beam theory. Both the divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter, mass ratio and spring stiffness.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.606-612
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• 1985

On the stability of the Beck's column with a tip mass, the influence of the characteristics of the springs at the fixed end of the column are studied. The equations of motion and boundary conditions of this system are established by using the Hamiton's principle. On the evaluation of the stability of the column, t he effect of the shear deformation and rotatory inertial is considered in calculation. For the maintenance of the stability of the column, it is proved that the constant of the translational spring at the fixed end must be very large while th magnitude of the constant of the rotational spring at the fixed end has no effect. When the constants of the springs at the fixed end are small, it is also proved that the influence of the moment of inertial of the tip mass on the stability of the column are decreased and for the translational spring the degree of the decrease is more and more. Therefore it is found that the characteristics of the springs at the fixed end are very effective elements for the stability of the column when the columns subjected to a compressive follower force are designed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.985-991
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• 2006

For a shear-deformable beam-column element subjected to non-conservative forces. equations of motion and a finite element formulation are presented applying extended Hamilton's principle. The influence of non-conservative force's direction parameter. internal and external damping forces, and shear deformation and rotary inertia effects on divergence and flutter loads of Beck's columns are intensively investigated based on element stiffness. damping and mass matrixes derived for the non-conservative system.