• Steel and Composite Structures
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• v.14 no.1
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• pp.73-83
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• 2013

In this paper Hamiltonian Approach (HA) have been used to analysis the nonlinear free vibration of Simply-Supported (S-S) and for the Clamped-Clamped (C-C) Euler-Bernoulli beams fixed at one end subjected to the axial loads. First we used Galerkin's method to obtain an ordinary differential equation from the governing nonlinear partial differential equation. The effect of different parameter such as variation of amplitude to the obtained on the non-linear frequency is considered. Comparison of HA with Runge-Kutta 4th leads to highly accurate solutions. It is predicted that Hamiltonian Approach can be applied easily for nonlinear problems in engineering.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.197-201
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• 2005

According to operating conditions of each engine, a PCV valve has various flow rates and pressure characteristic. In a developed country, it has been developing by a computational design simulation. But, Korean companies have no ability of technical design for a PCV valve. So, they depend on their experiments and copy the designs of foreign companies when they need to design new PCV valves. These problems cause increase of error rate and take much time. Hence, optimal design for a PCV valve is needed to secure for continuous competition against foreign automobile companies. In this study, we used 4th order Runge-Kutta method for the prediction of spool movements and applied Bernoulli's equation for the determination of flow area. A spool geometry and spool displacement were predicted to be satisfied in comparison with their experiment.

• Journal of Auto-vehicle Safety Association
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• v.5 no.1
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• pp.25-30
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• 2013

The main purpose of this research is to predict dynamic behavior of door locking system for side impact safety and the design process to avoid door opening is introduced. The equations of motion that represent the system are obtained from the energy equation. From them, the motion of door handle is predicted by using Runge-Kutta $4^{th}$ order method and the simulation result is compared with the real crash data. Also, the design guide to define the properties of door locking system from the standpoint of avoiding door opening phenomenon is introduced.

• Applied Chemistry for Engineering
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• v.9 no.7
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• pp.1079-1084
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• 1998

Reaction kinetics between 4,4'-dihexyl methane diisocyanate($H_{12}MDI$) and n-hexanol in toluene with dibutyltin dilaurate(DBTDL) as catalyst was studied by experimental measurements and mathematical modeling. Experiments were carried out at various temperatures, catalyst concentrations and [NCO]/[OH] ratios, and the reaction kinetics were described by two second-order reactions, the one between NCO and OH leading to urethane and the other between urethane and NCO leading to allophanate. The rate constants were estimated by the Runge-Kutta 4th-order method. Experiments and mathematical simulations showed a good agreement for various experimental conditions. The [allophanate]/[urethane] ratios at 90% conversion of initial NCO were estimated to be over 20% for most conditions employed in the present study, indicating that allophanate formation might significantly affect the properties of urethane polymers.

• 한국전산유체공학회:학술대회논문집
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• 2007.10a
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• pp.249-257
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• 2007

A high resolution numerical method aimed at solving gas-liquid two-phase flow is proposed and applied to gas-liquid two-phase shock tube problem. The present method employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. By applying the homogeneous equilibrium cavitation model, the present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation and large density changes. The speed of sound for gas-liquid two-phase media is derived on the basis of thermodynamic relations and compared with that by eigenvalues. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media and some data related to computational efficiency are made. Comparisons of predicted results and exact solutions are provided and discussed.

• Journal of computational fluids engineering
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• v.12 no.2
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• pp.53-62
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• 2007

A high resolution numerical method aimed at solving cavitating flow is proposed and applied to gas-liquid two-phase shock tube problem. The present method employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. By applying the homogeneous equilibrium cavitation model, the present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation and large density changes. The speed of sound for gas-liquid two-phase media is derived on the basis of thermodynamic relations and compared with that by eigenvalues. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media at isothermal condition and some data related to computational efficiency are made. Comparisons of predicted results and exact solutions are provided and discussed.

• Journal of Astronomy and Space Sciences
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• v.5 no.1
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• pp.19-30
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• 1988

The existence of the j-type collision periodic orbit is examined on the condition of mass ratio 0.9878449 and Jacobian constant 2.9∼3.4. Using the Birckhoff's regularization method and the 5th order Runge-Kutta variable step-sized numerical roution introduced by Fehlberg (1968). we test their periodicities. As the results, 4 j-type collision orbits and 5 peculiar orbits are represented. There are good agreements in this collision orbits with the relationship between the period and the shape of orbit proposed by Pinotsis Zikides(1984).

• The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.7 no.2
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• pp.31-35
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• 1993

The radial density distributions of the positive column of strongly modulated low -pressure gas discharges in mercury - rare gas mixtures at 10 tom pressure have been studied theoretically. The current was modulated inusoidally with a modulation depth of 50%. Calculations have shown that the radial profile of the excited atoms is ditferent form 0th Bessel function $J_0$(2.4r/R) and the invertion of the radial distribution of the excited atom can occur at some frequency. The hybrid method of FDM and 2nd order Runge-Kutta meth od is used for solving differenzial equations.

• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.4
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• pp.42-49
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• 2004

When a truck cab is conveyed at a constant speed by a hanger and immersed into the painting reservoir, it may fall off from the hanger by buoyancy. In order to reduce the buoyancy, on the bottom of a cab panel are holes placed, which allow paint to flow into the inside of a cab. In this study, a differential equation is derived which can be solved numerically by using 4th-Order Runge-Kutta method to calculate transient behavior of the buoyant force with sizes and locations of the holes given. The solution is utilized to optimally determine sizes and locations of the holes.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.2
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• pp.101-107
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• 2012

In this study, Constraint Force Equation Methodology (CFEM) is used to develop a multi-body dynamic analysis program with constraints. Seven constraint models are implemented to analyze constraint motions of multiple bodies. The augmented equations with the constraints are solved with the 4th order Runge-Kutta method for higher degree of accuracy. The analysis code is verified by comparing the analysis results of the motion of bodies with various constraints to published results.