• Earthquakes and Structures
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• 제7권1호
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• pp.1-15
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• 2014

In this paper we consider three different cases and we apply Variational Approach (VA) to solve the non-natural vibrations and oscillations. The method variational approach does not demand small perturbation and with only one iteration can lead to high accurate solution of the problem. Some patterns are presented for these three different cease to show the accuracy and effectiveness of the method. The results are compared with numerical solution using Runge-kutta's algorithm and another approximate method using energy balance method. It has been established that the variational approach can be an effective mathematical tool for solving conservative nonlinear dynamical equations.

• 한국컴퓨터정보학회논문지
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• 제8권3호
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• pp.66-72
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• 2003

상미분 방정식은 물리학, 기계학, 전기학, 열역학 등에 많이 이용되는 방정식이나 수식이 복잡하고 처리 속도가 늦어서 실시간 처리에 어려움이 많다. 그래서 이 논문에서는 소프트웨어적인 방법으로는 많은 계산량으로 인하여 처리 속도가 떨어지므로 시스토릭어레이를 이용하여 Runge-Kutta 방법으로 상미분 값을 구하는 새로운 하드웨어를 제안하였다. 이 제안한 하드웨어는 처음 셀에서의 입력이 연속적으로 각 셀을 거치면서 처리되어 마지막셀에서는 상미분 값을 얻을 수 있다. 이렇게 처리함으로서 기존의 소프트웨어적인 방식에 비하여 수렴 속도도 빠르고 정확한 근사 값을 구할 수 있으므로 실시간 처리에 많이 이용될 수 있을 것이며, 기존의 다른 수치처리를 하는 하드웨어와 통합하여 사용될 수 있다. 이 논문에서는 제안한 하드웨어를 시뮬레이션하여 정확한 결과가 나오는 것을 확인하였다.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• Structural Engineering and Mechanics
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• 제75권2호
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• pp.239-246
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• 2020

In this paper, a novel analytical method, Max-Min Approach (MMA), has been presented and applied to consider the nonlinear vibration of dry cask storage systems. The nonlinear governing equation of the structure has been developed using the shell theory. The MMA results are compared with numerical solutions derived by Runge-Kutta's Method (RKM). The results indicate a satisfying agreement between MMA and numerical solutions. Parametric studies have been conducted on the nonlinear frequency of dry casks. The phase-plan of the problem is also presented and discussed. The proposed approach can potentially ca be extended to highly nonlinear problems.

• 한국농공학회지
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• 제36권2호
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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.

• 한국해양공학회지
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• 제14권1호
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• pp.67-73
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• 2000

The dynamic behavior of a moving elastic body system with three constant velocitics on a simple beam with an axial load is analyzed by numerical method. A moving elastic body system is composed of an elastic body and a suspension unit with two unsprung masses. The governing equations are derived with an aid of Lagrange's equation. These equation are solved by Runge-Kutta method. The damping coefficients a spring constants of the suspension unit the force circular frequency on a moving elastic body the velocity of a moving elastic body system. These effects are more important in the high modes of a simple beam.

• 정보처리학회논문지B
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• 제13B권1호
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• pp.15-20
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• 2006

이 논문은 컴퓨터 게임을 위한 물리 엔진의 성능 향상 및 이를 적용한 지능적인 게임 캐릭터에 관한 연구를 서술한다. 물리적 상황을 자동으로 인식하는 알고리즘으로는 Momentum back-propagation을 적용하였다. 또한 우리는 각 상황에 따른 적분 방식의 실험 결과를 제시한다. 실험을 위하여 Euler Method, Improved Euler Method, 및 Runge-kutta Method의 세 가지의 적분 방식을 적용하였다. 각 적분 방식의 실험 결과에서 충돌이 없는 상황에서는 Euler Method가 최적의 성능을 보여주었다. 또한 충돌 상황에서는 세 가지 방식이 모두 비슷한 성능을 보여주었지만, Runge-kutta Method가 최적의 정확도를 보여주었다. 물리 상황인식에 대한 실험결과에서는 입력 층과 출력 층이 고정된 상태에서 은닉 층이 3일 때 가장 좋은 성능을 보여주었고, 또한 학습횟수가 30000일 때 최적의 성능을 보여주었다. 앞으로 우리는 다른 장르의 게임에 이러한 물리적 컨텍스트(context)를 인식하는 연구를 진행할 것이며 또한 전체 게임의 성능을 증가할 수 있도록 M-BP이외의 인식 알고리즘을 적용할 것이다.

• 한국전산유체공학회지
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• 제19권3호
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• pp.91-97
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• 2014

A high resolution numerical method aimed at solving cavitating flow was proposed and applied to gas-liquid two-phase shock tube problem with arbitrary void fraction. The present method with compressibility effects employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. The Jacobian matrix from the inviscid flux of constitute equation is diagonalized analytically and the speed of sound for the two-phase media is derived by eigenvalues. So that the present method is appropriate for the extension of high order upwind schemes based on the characteristic theory. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results of high speed flow phenomena 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 solutions at isothermal condition are provided and discussed.

• 한국해양공학회지
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• 제9권2호
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• pp.53-60
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• 1995

A multi-leg spread mooring system for floating offshore structures is important, but the multi-leg static analysis is complicated due to the nonlinear behavior of each line and the effect of current which affects each line differently. The pretensioned position of the multi-leg mooring system obtained from the static equilibrium condition changes into a different position due to external loads and current. In this paper, the new position and the static tension at each line are caculated. The relation between the initial static equilibrium position and the new position due to the external loads is expressed in terms of the Taylor's series expansion. The Runge-Kutta $4^{th}$ method is employed in analyzing the 3-dimensional static cable nonlinear equations.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1991년도 하계학술대회 논문집
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• pp.682-686
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• 1991

The purpose of a solar tracking system (STS) is to control the attitude of a space vehicle so that it will track the sun with high accuracy. In this paper, the literature of tracking of the sun in a plane is surveyed and a control modeling for the analysis of STS is presented by simultaneous transfer functions and state-space equations. Also a program for obtaining state variables by the single term Walsh series(STWS) approach is developed. The proposed approach is much simpler in analysis and easier in implementation than the Runge-Kutta numerical integration Method. The results of computer simulation are shown for the dynamic behaviors of vehicle axis, armature-controlled dc motor and controller of STS via a Runge-Kutta method and a single term Walsh series approach, respectively.