• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.6
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• pp.871-883
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• 1997

Kinetodynamics of a cam driving slider mechanism consists of kinematic analysis and force analysis. The kinematic analysis is to determine the kinematic characteristics of a cam driving mechanism and a slider mechanism. The force analysis is to determine the joint forces of links, the contact forces of the cam and follower, and the driving torque of a main shaft. This paper proposes a close loop method and a tangent substitution method to formulate the relationships of kinematic chains and to calculate the displacement, velocity and acceleration of the cam driving slider mechanism. Also, and instant velocity center method is proposed to determine the cam shape from the geometric relationships of the cam and the roller follower. For dynamic analysis, the contact force and the driving torque of the cam driving slider mechanism are calculated from the required sliding forces, sliding motion and weight of the slider.

• Journal of the Korea institute for structural maintenance and inspection
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• v.8 no.1
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• pp.195-202
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• 2004

The shell due to the effect of initial normal pressures on the shell surface was based on the assumption that the directions of the pressures are always normal to the undeformed shell surface, and that the change in the surface area of the shell is negligible. But the fact that the pressure are always normal to the deforming surface leads "follower force". The follower effect in the analysis can significantly alter the solution for natural frequency and buckling load as compared to the case when the direction of the pressures are assumed to be normal to the uniform shell surface. The expression for the part of strain energy contribution from normal pressure due to the effect of follower force was derived and added to the element stiffness matrix of axisymmetric shell. In the case of increasing external pressure, the natural frequencies decrease until one of them reaches zero. Theoretically the smallest applied load that reduces the frequency of any mode to zero, will have same magnitude as that of the buckling load. In order to determine the bucking load of the shell a few sets of frequencies are computed and the results considering the follower effects are well with the exact solution while the case without that are quite different. But in case of hemispherical dome, there are little difference in buckling pressure between with and without the effect of follower force.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1992.10a
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• pp.215-219
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• 1992

This paper presents a motion coordination of two robot manipulators coordinating an object. To coordinate the object, a force/position control scheme in a mode of leaer/follower is devised. The dynamics of the object are incorporated into the dynamics of the leader arm, which yields a reduced order model of two arm system. In order to regulate interaction forces between two arm, the dynamics of the follower arm are expressed as force dynamic equations such that a novel direct forces between two arms and two different type of bounded input disturbances, boundedness and asymptotic stability results based on a proposed Lyapunov function are shown. Also, a sufficient condition for a stability robustness is derived based on the Lyapunov approach.

• Journal of KSNVE
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• v.10 no.5
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• pp.865-872
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• 2000

This paper presents the modeling, theoretical formulation, and stability analysis for a combined system of a spinning disc and a head that contacts the disc. In the analytic model, head interference is considered by a rotating mass-spring-damper system together with a frictional follower force on the damped annular discs. The multiple scale method is utilized to perform the stability system that shows the existence of instability associated with parametric resonances. Using the formulated system , instability regions of optical recording disc are investigated with variation of mass, stiffness and friction force of a head, respectively. The simulation results show that the stiffness of a head is the most sensitive parameter on the instability of the disc.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.9
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• pp.1352-1358
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• 2004

The mechanical spring is one of widely used machine elements. Among various kinds, flat-type spring loaded by a rotating pin was studied. A flat spring was simplified to a cantilever beam, and numerical analysis was attempted. Since the loading pin rotates about a separate axis from the fixed spring or vice versa, the location, direction, and magnitude of the contact force including normal contact and friction loads vary accordingly. Meanwhile, the spring is deformed substantially as the relative motion progresses. Therefore, this problem needs to be formulated taking the follower loading characteristics and geometrical non-linearity into account. Derived nonlinear differential equation was solved to yield the spring deflection, contact force and the torque to rotate the pin, and the result was compared with a finite element solution. Also, the influences of principal design parameters were studied. The proposed methodology is expected to be useful for the design of pin-loaded flat spring and the prevention of mechanical failures in the form of yielding or fatigue failure of spring or severe wear of the components.

• Journal of Korean Association for Spatial Structures
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• v.2 no.1 s.3
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• pp.93-102
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• 2002

Pressure loads caused by gas, water and wind are the most important load cases in structural analysis. Often the pressure loads are approximated by constant directional loads since it is difficult to evaluate the exact value. However, the pressure load is defined as a displacement dependent one and it is necessary to consider the follower effects of the load in analysis procedure. In this study, the large deformation analysis considering geometrical nonlinearity for shell structures under pressure loads is presented. Finite element by using a three-node flat triangular shell element is formulated and the follower effects of the pressure load are included in the formulation. Some of results are presented for cantilevered beam under uniform external pressure and thin circular ring under non-uniform external pressure. The present results are in good agreement with the results available in existing literature and commercial software ABAQUS.

• Steel and Composite Structures
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• v.6 no.2
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• pp.87-101
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• 2006

The deformation and dynamic behavior mechanism of submerged shell-like lattice structures with membranes are in principle of a non-conservative nature as circulatory system under hydrostatic pressure and disturbance forces of various types, existing in a marine environment. This paper deals with a characteristic analysis on quasi-periodic and chaotic behavior of a circular arch under follower forces with small disturbances. The stability region chart of the disturbed equilibrium in an excitation field was calculated numerically. Then, the periodic and chaotic behaviors of a circular arch were investigated by executing the time histories of motion, power spectrum, phase plane portraits and the Poincare section. According to the results of these studies, the state of a dynamic aspect scenario of a circular arch could be shifted from one of quasi-oscillatory motion to one of chaotic motion. Moreover, the correlation dimension of fractal dynamics was calculated corresponding to stochastic behaviors of a circular arch. This research indicates the possibility of making use of the correlation dimension as a stability index.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.695-700
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• 2000

The dynamic stability of spinning beam with free boundary conditions for both edges subjected to a tip follower force $P_0+P_1cos{\Omega}t$ is analyzed. It is studied that the beam has a concentrated mass. and then the effects of the axial locations of the mass are studied. The beam is modelled with the Timoshenko type shear deformations. The Hamilton's principle is used to derive the equations of motion, and the critical spinning speed of a beam subjected to a follower force with various non-dimensional parameters is investigated. The finite elements are used with $C^0$ continuity to analyze the spinning beam model, and the method of multiple scales is tried to investigate the dynamic instability regions. The governing equations of motion involve periodic coefficients, which are not in the form of standard Mathieu-Hill equations. The result shows that the concentrated mass increases the dynamic stability of the spinning free-free beam subjected to a thrust.