• Steel and Composite Structures
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• 제14권1호
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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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• 한국전산유체공학회 2005년도 춘계 학술대회논문집
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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.

• 자동차안전학회지
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• 제5권1호
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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.

• 공업화학
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• 제9권7호
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• pp.1079-1084
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• 1998

우레탄 생성반응의 동역학을 조사하기 위해 지방족 이소시아네이트인 4,4'-dihexyl methane diisocyanate($H_{12}MDI$)와 1 관능기 알코올인 n-hexanol간의 반응을 실험적 측정과 수학적 모델링을 통해 연구하였다. 실험은 dibutyltin dilaurate(DBTDL)을 촉매로, 톨루엔을 용매로 온도, 촉매농도, [NCO]/[OH] 비 등을 변화시키면서 실시하였고, 반응동역학은 NCO기와 OH기의 반응에 의한 우레탄 생성반응 및 NCO기와 우레탄간의 반응에 의한 allophanate 생성반응 등 2가지 2차반응식으로 모사하였다. 반응속도상수는 Runge-Kutta 4th order 방법에 의한 전산모사방법으로 계산하였다. 대부분의 조건에서 실험치와 계산치가 잘 일치하여 본 연구에서 제안하는 반응 모델과 속도상수 계산방법이 적절함을 알 수 있었다. 또한 NCO기 90% 전환율에서 allophante/urethane의 비를 계산하였는데 대부분의 조건에서 20% 이상의 높은 값이 얻어져 allophanate 생성반응이 우레탄 물성에 중요한 영향을 미칠 수 있음을 알 수 있었다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2007년도 추계 학술대회논문집
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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.

• 한국전산유체공학회지
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• 제12권2호
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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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• 제5권1호
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• pp.19-30
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• 1988

지구-달계의 질량비인 $\mu$-0.9878449 와 Jacobi 상수 2.9~3.4인 범위의 조건일 때 j종족 충돌궤도가 존재하는가를 조사하였다. 수치적인 방법으로는 Birckhoff의 정칙화 평면에서 Fehlberg(1968)의 5차 Runge-Kutta가변구간 수치적분방법을 사용하여 궤도의 주기성을 검증하였다. 그 결과 4개의 j종족 충돌궤도와 5개의 특이형궤도를 얻었고, 또한, 이 j 종족 충돌궤도가 Pinotsis와 Zikides(1984)가 제시한 주기와 궤도형태의 상관관계를 보였다.

• 한국조명전기설비학회지:조명전기설비
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• 제7권2호
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• pp.31-35
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• 1993

본 논문은 t은과 10[torr]의 희유기체의 혼합기체 중에서 심하게 변조된 저압기체방전의 양광주의 반경방향 압자분포를 이론적으로 연구하였다. 전류는 깊이 50[%[로 정현파로 변조되었다. 계산결과 여기 원자의 반경방향 분포는 0차 Bessel 함수 $J_0(2.4r/R)$와 다르고 분포의 반전이 나타나는 주파수 대역도 있었다. 연립미분방정식을 풀기 위하여 FDM과 2계 Runge-Kutta method의 혼합법을 사용하였다.

• 한국자동차공학회논문집
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• 제12권4호
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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.

• 한국항공우주학회지
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• 제40권2호
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• pp.101-107
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• 2012

본 연구에서는 CFEM을 이용하여 구속조건이 있는 다물체의 운동방정식해석 프로그램을 개발하였다. 다양한 구속조건을 다루기 위하여 7개의 구속모델이 적용되었다. 구속조건으로 보안된 운동방정식은 높은 정확도를 위해 4차의 Runge-Kutta 방법을 사용하여 해석하였다. 다양한 구속조건이 있는 문제에 대하여 개발된 프로그램을 적용하고, 발표된 결과와 비교함으로써 개발 프로그램을 검증하였다.