• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.547-550
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• 2005

In many machines handling lightweight and flexible media, such as automated teller machines and printers, the media must transit an open space. It is important to predict the static and dynamic behavior of the sheets with a high degree of reliability The nonlinear theory of the dynamic elastica has often been used to a nonlinear dynamic deflection model. In this paper, the governing equation is derived and simulated by the finite difference method. The analysis has to include aerodynamic effect for more exact behavior analysis, because the flexible media can be deformed drastically by a little force. Therefore aerodynamic force must be applied to the governing equation. Different results were obtained with and without aerodynamic effect and the resulted show that after contacting circular guide, the directions of flexible media of two cases are different.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.569-572
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• 2005

In many machines handling lightweight and flexible media, such as automated teller machines(ATM) and printers etc., the media must transit an open space. In the paper feeding mechanism, it is important to feed the sheet without jamming under any conditions. To avoid sheet jamming, first we need to predict the behavior of the sheet exactly. The nonlinear theory of the dynamic elastica has often been used to a nonlinear dynamic deflection model. In this paper, the governing equation is derived and simulated by the finite difference method. The analysis has to include aerodynamic effect for more exact behavior analysis. For verification of the numerical simulation, the experiments were performed using high-speed camera and feeding mechanism. The experimental results show good agreement with the numerical simulations.

• Computational Structural Engineering
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• v.10 no.4
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• pp.177-184
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• 1997

In this paper, numerical methods are developed for solving the elastica of simple beams with variable-arc-length subjected to a point loading. The beam model is based on Bernoulli-Euler beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to solve the governing differential equations and to compute the beam's rotation at the left end of the beams. Extensive numerical results of the elastica responses, including deflected shapes, rotations of cross-section and bending moments, are presented in non-dimensional forms. The possible maximum values of the end rotation, deflection and bending moment are determined by analyzing the numerical data obtained in this study.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.6A
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• pp.617-624
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• 2009

This study deals with the free vibrations of the elastica shaped arch with linear taper. The shape of elastica is obtained from the Bernoulli-Euler beam theory. Differential equations governing free vibrations of such arch are derived and numerically solved to determine natural frequencies, in which three kinds of taper type and two kinds of end constraint, respectively, are considered. For validating the theories presented herein, the frequency parameters obtained in this study are compared to those of SAP 2000. As results of the numerical analyses, effects of end constraint, taper type, slenderness ratio and section ratio on the lowest four non-dimensional frequency parameters are extensively investigated.

• Structural Engineering and Mechanics
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• v.32 no.4
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• pp.501-516
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• 2009

This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on Kirchhoff's rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance ($10^{-5}$). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.529-539
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• 1997

This paper deals with the bending problem of a variable-are-length elastica under moment gradient. The variable are-length arises from the fact that one end of the elastica is hinged while the other end portion is allowed to slide on a frictionless support that is fixed at a given horizontal distance from the hinged end. Based on the elastica theory, exact closed-form solution in the form of elliptic integrals are derived. The bending results show that there exists a maximum or a critical moment for given moment gradient parameters; whereby if the applied moment is less than this critical value, two equilibrium configurations are possible. One of them is stable while the other is unstable because a small disturbance will lead to beam motion.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.600-605
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• 2004

In many machines handling lightweight and flexible media such as magnetic tape drives, xerographic copiers and sewing machines, the media must transit an open space. It is important to predict the static and dynamic behavior of the sheets with a high degree of reliability. The nonlinear theory of the dynamic elastica has often been used to a nonlinear dynamic deflection model. In this paper, the governing equation is derived and simulated by the finite differential method. The parametric cubic curve is applied for defining the guide shape. The dynamic contact conditions suggested by Klarbring is used to predict the direction of the flexible media according to the initial velocity and the friction coefficient. The analysis is also compared to the conventional model, showing that after contacting a $45^{\circ}$ wall, the directions of flexible media of two models are different.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.2
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• pp.56-66
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• 1994

Numerical methods are developed to obtain the buckling loads and to analyze the postbuckling behavior of the tapered steel piles. The nondimensional differential equations governing the elastica of the buckled piles are derived by the third order theory and solved numerically. The Runge-Kutta method is used to solve the differential equations, and the bisection method is used to obtain the buckling loads and the reaction moments of the clamped ends. Both the linear and stepped taper of the steel piles are considered as the variable crosssection in the differential equations. As the numerical results, the equilibrium paths, the buckling loads vs. section ratio curves and the typical elastica and the bending moment diagrams of the buckled piles are presented in figures. Experimental studies that complement the theoretical results are presented. It is expected that the numerical methods developed in this study for calculating the buckling loads and analyzing the postbuckling behavior of the steel piles are used in the structural and foundation engineering.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.201-208
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• 2000

This paper explores the non-linear behavior of tapered beam subjected to a floating concentrated load. For applying the Bernoulli-Euler beam theory to this beam, the bending moment at any point of elastica is obtained from the final equilibrium state. By using the bending moment equation and the Bernoulli-Euler beam theory, the differential equations governing the elastica of clamped-roller beam are derived, and solved numerically. Three kinds of tapered beam types are considered. The numerical results of the non-linear behavior obtained in this study are agreed quite well to the results obtained from the laboratory-scale experiments.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.2 s.95
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• pp.206-212
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• 2005

In many machines handling lightweight and flexible media, such as magnetic tape drives, xerographic copiers and sewing machines, the media must transit an open space. It is important to predict the static and dynamic behavior of the sheets with a high degree of reliability. The nonlinear theory of the dynamic elastica has often been used to a nonlinear dynamic deflection model. In this paper, the governing equation is derived and simulated by the finite difference method. The parametric cubic curve is applied for defining the guide shape. The dynamic contact conditions suggested by Klarbring is used to predict the direction of the flexible media according to the initial velocity and the friction coefficient. The analysis is also compared to the conventional model, showing that after contacting a $45^{\circ}$ wall, the directions of flexible media of two models are different.