• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.202-206
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• 2001

The paper presents the dynamic stability of a vertical cantilevered pipe conveying fluid and having an intermediate translational linear spring. The translational linear spring can be located at an arbitrary position. Governing equations are derived by energy expressions, and numerical technique using Galerkin's method is applied to discretize the equations of small motion of the pipe. Effects of linear spring supports on the dynamic stability of a vertical cantilevered pipe conveying fluid are fully investigated for various locations and magnitudes of the translational linear spring.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.815-818
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• 2006

This paper deals with the free, in-plane vibrations of curved members with the translational(radial and tangential directions) and rotational springs at the ends. The governing differential equations for the circular curved member are solved numerically using the corresponding boundary conditions. The lowest three natural frequencies and the corresponding mode shapes are obtained over a range of non-dimensional system parameters: the subtended angle, the slenderness ratio, the translational spring stiffness, and the rotational spring stiffness.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.802-807
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• 2003

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and tip masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the translational spring parameter, the rotational spring parameter, the mass ratio and the dimensionless mass moment of inertia.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.6
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• pp.1496-1502
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• 1994

The influences of spring position and spring stiffness on the critical force of a cantilevered beam subjected to a follower force are investigated. The spring attatched to the beam is assumed to be a translational one and can be located at arbitrary positions of the beam as it has not been assumed so far. The effects of transeverse shear deformation and rotary intertia of the beam are also included in this analysis. The charateristic equation for the system is derived and a finite element model of the beam using local coordinates is formulated through extended Hamilton's principle. It is found that when the spring is located at position less than that of 0.5L, the flutter type instability only exists. It is shown that the spring position approaches to the free end of the beam from its midpoint, instability type is changed from flutter to divergence through the jump phenomina according to the increase of spring stiffness.

• Journal of the Korean Society of Safety
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• v.13 no.4
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• pp.49-58
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• 1998

On the stability of the Timoshenko cantilever column subjected of a compressive follower force, the influences of the moment of inertia of the tip mass at the free end and the characteristics of a translational spring at the free end of the column are studied. The equations of motion and boundary conditions of system are estabilished by using the d'Alembert virtual work of principle. On the evaluation of stability of the column, the effect of the shear deformation and rotatory inertia is considered in calculation. The moment of inertia of the tip mass at the free end of the column is changed by adjusting the distance c, from the free end of the column to the tip mass center. The free end of the column is supported elastically by a translational spring. For the maintenance of the good stability of the column, it is also proved that the constant of the translational spring at the free end must be very large for the case without a tip mass while it must be small for the case with a tip mass. Therefore, it is found that the shape of the tip mass and the characteristic of the spring at the free end are very effective elements for the stability of the column when the columns subjected to a compressive follower force are designed.

• Journal of KSNVE
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• v.7 no.1
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• pp.91-97
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• 1997

An analysis is presented on the stability of an elastic cantilever column having the elastic restraints at its free end, carrying an added tip mass, and subjected to uniformly distributed follower forces. The elastic restraints are formed by both a translational spring and a rotatory spring. 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 this elastic system. The added tip mass increases as a whole the critical flutter load of the elastic cantilever column, but the presence of its moment of inertia of mass has a destabilizing effect. The existence of the translational and rotatory springs at the free end increases the critical flutter load of the elastic cantilever column. Nevertheless, their effects on the critical flutter load are not uniform because of their coupling. The translational spring restraining the free end of the cantilever column decreases the critical flutter load by coupling with a large value of tip mass, while by coupling with the moment of inertia of tip pass its effect on the critical flutter load is contrary. The rotatory spring restraining the free end of the cantilever column increases the critical flutter load by coupling with the tip mass, but decreases it by coupling with the moment of inertia of the tip mass.

• Journal of Mechanical Science and Technology
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• v.20 no.9
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• pp.1382-1389
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• 2006

Dynamic responses of a simply supported beam with a translational spring carrying a moving mass are studied. Governing equations of motion including all the inertia effects of a moving mass are derived by employing the Galerkin's mode summation method, and solved by using the Runge-Kutta integral method. Numerical solutions for dynamic responses of a beam are obtained for various cases by changing parameters of the spring stiffness, the spring position, the mass ratio and the velocity ratio of a moving mass. Some experiments are conducted to verify the numerical results obtained. Experimental results for the dynamic responses of the test beam have a good agreement with numerical ones.

• Journal of Ocean Engineering and Technology
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• v.6 no.1
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• pp.69-77
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• 1992

The natural frequencies of a beam on elastic foundation are investigated in the present paper. The inhomogeneous elastic foundation can be modelled as a combination of distributed translational spring, rotational spring, intermediate supports and dampers. The natural frequencies and mode shapes of the system are obtained by using the Galerkin's method, and also compared with the results in the literature. Furthermore, the natural frequencies of the beam with elastically mounted masses, which can be used as vibration absorbers, are obtained by an efficient numerical scheme suggested in the present paper.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.181-185
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• 2001

This paper deals with the dynamic stability of a disc brake pad taking into account of its shear deformation and rotary inertia. A brake pad can be modeled as a beam like model subjected to distributed friction forces and having two translational springs. The study of this model is intended to provide a fundamental understanding of dynamic stability of drum brake pad. Governing equations of motion are derived from extended Hamilton's principle and their corresponding numerical solutions are obtained by applying the finite element formulation. The critical distributed friction force and the instability types are investigated bt changing two translational spring constants, rotary inertia parameter and shear deformation parameter. Also, the changes of eigen-frequencies of a beam determining instability types are investigated for various combinations of two translational spring constants.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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• pp.309-315
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• 1996

An analysis is presented on the stability of elastic cantilever column subjected to uniformly distributed follower forces as to the influence of the elastic restraints and a tip mass at the free end. The elastic restraints are formed by both the translational and 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 this elastic system. The added tip mass increases as a whole the critical flutter load in this system, but the presence of its moment of inertia of mass has a destabilizing effect. The existence of the translational and rotatory spring at the free end increases the critical flutter load of the elastic cantilever column. Nevertheless their effects on the critical flutter load are not uniform because of their coupling. The translational spring restraining the end of cantilever column decreases the critical flutter load by coupling with a large value of tip mass, while by coupling with the moment of inertia of tip mass its effect on the critical flutter load is contrary. The rotatory spring restraining the free end of cantilever column increases the critical flutter load by coupling with the tip mass, but decreases it by coupling with the moment of inertia of tip mass.