• 대한토목학회논문집
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• 제41권1호
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• pp.39-48
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• 2021

본 논문에서는 정적 수직하중을 받는 barrette 말뚝의 고유진동수를 산정할 수 있는 해석모델을 제안하였다. 비균질 지반에 설치된 직사각형 마찰말뚝의 자유진동을 지배하는 미분방정식을 유도하였다. 이 지배방정식을 Runge-Kutta 법을 이용하여 수치적분하였고, 미분방정식의 고유치인 고유진동수는 Regula-Falsi 법을 이용하여 산정하였다. 말뚝의 고유진동수는 유한요소해석의 결과와 잘 일치하였다. 말뚝의 고유진동수를 증가시키는 말뚝변수는 단면형상비, 마찰저항비, 지반강성비이고, 감소시키는 말뚝변수는 마찰형상비, 세장비, 압축계수이다.

• 융합정보논문지
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• 제11권3호
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• pp.132-139
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• 2021

고감쇠 차량이 둔턱(bumped barrier)을 넘어갈 때 발생하는 강제 진동의 응답 특성이 연구되었고, 이와 관련하여 특히 강제 진동 차량에서 변위, 속도 및 가속도의 응답 거동을 분석하였다. 또한, 각각의 응답을 얻기 위해 Runge-Kutta-Gill의 수치해석법을 수행하여 시간영역의 분석을 하였다. 강제 진동 모델의 여러 고감쇠 조건으로 응답 특성을 얻을 수 있었고 질량, 감쇠 및 강성을 달리하여 수치 분석 후, 임펄스 충격력으로 차체에 가해지는 모델을 고려하여 강제력에 의한 차량 모델의 응답 특성을 얻었고 실험 결과와 비교하여 그 모델의 타당성을 밝혔다. 진폭 및 차량의 고유진동수도 고려하여 분석하였고 차량 모델의 나이키스트 선도를 구하여 고감쇠의 정도에 따라 특성을 분석할 수 있었다. 상이한 질량, 감쇠 및 강성에 따라 임펄스 충격력에 의한 강제 진동 응답 특성을 분석하였다.

• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.629-645
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• 2020

A uniformly convergent numerical method is developed for solving singularly perturbed 1-D parabolic convection-diffusion problems. The developed method applies a non-standard finite difference method for the spatial derivative discretization and uses the implicit Runge-Kutta method for the semi-discrete scheme. The convergence of the method is analyzed, and it is shown to be first order convergent. To validate the applicability of the proposed method two model examples are considered and solved for different perturbation parameters and mesh sizes. The numerical and experimental results agree well with the theoretical findings.

• 충청수학회지
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• 제28권4호
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• pp.623-633
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• 2015

In this paper, a general Weighted Essentially Non-Oscillatory (WENO) interpolation is proposed and applied to a semi-Lagrangian method. The proposed method is based on the conservation law, and characteristic curves are used to complete the semi-Lagrangian method. Therefore, the proposed method satisfies conservation of mass and is free of the CFL condition which is a necessary condition for convergence. Using a several standard examples, the proposed method is compared with the third order Strong Stability Preserving (SSP) Runge-Kutta method to verify the high-order accuracy.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.2060-2065
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• 2003

Aeolian tone generation from a two dimensional circular cylinder is numerically investigated via direct numerical simulation and hydrodynamic-acoustic splitting method. All governing equation are spatially discretized with the sixth-order compact scheme and fourth-order Runge-Kutta method to avoid excessive numerical dissipations and dispersions of acoustic quantities. Comparisons of two results show that the previous splitting method can not accurately predict the aeroacoustic noise of wall bounded shear flow. In this study, a perturbation viscous term and a new energy equation have been developed. This modified splitting method accurately predicts aeroacoustic noise from wall-bounded shear flow. The present results agree very well with the direct numerical simulation solution.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.793-798
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• 2001

This paper is basic study of seismic response analysis for the large scaled structures subjected to seismic loading. The authors propose seismic response analysis algorithm for the multi-story structures, which are subjected to ground acceleration. This analysis method is derived from an combination of the transfer stiffness coefficient method(TSCM) and Newmark method. Numerical computation is performed for simple multi-story structures acting on an arbitrary ground acceleration. Numerical results by the TSCM which is applied to the various strong ground motion are compared with results by central difference method and Runge- Kutta method.

• Structural Engineering and Mechanics
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• 제42권4호
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• pp.449-469
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• 2012

For generally damped linear systems with repeated eigenvalues and defective eigenvectors, this study provides a decomposition method based on residue matrix, which is suitable for engineering applications. Based on this method, a hybrid approach is presented, incorporating the merits of the modal superposition method and the residue matrix decomposition method, which does not need to consider the defective characteristics of the eigenvectors corresponding to repeated eigenvalues. The method derived in this study has clear physical concepts and is easily to be understood and mastered by engineering designers. Furthermore, this study analyzes the applicability of step-by-step methods, including the Newmark beta and Runge-Kutta methods for dynamic response calculation of defective systems. Finally, the implementation procedure of the proposed hybrid approach is illustrated by analyzing numerical examples, and the correctness and the effectiveness of the formula are judged by comparing the results obtained from the different methods.

• 전기학회논문지
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• 제61권8호
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• pp.1123-1129
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• 2012

This paper presents the fast steady state analysis using time-stepping finite element method for a high power three-phase transformer. The high power transformer spends huge computational cost of the time-stepping finite element method. It is because that the high power transformer requires a lot of time to reach steady state by its large inductance component. In order to reduce computational cost, in this paper, the adaptive time-step control algorithm combined with the embedded 2nd 4th singly diagonally implicit Runge-Kutta method and the analysis strategy using variation of the winding resistance are studied, and their numerical results are compared with those from the typical time-stepping finite element method.

• International Journal of Ocean System Engineering
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• 제3권3호
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• pp.111-115
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• 2013

Blasius equation describes the boundary layer formed over a flat plate inside a fluid and this equation is solved numerically by the method of moments which is a type of weighted residual methods. Compared to the traditionally used Runge - Kutta Method, Method of Moments propose a direct solution to Blasius Equation which makes it easier to solve. The obtained solutions show good agreement with the results found in literature and this study aims to demonstrate the power of the method.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.753-765
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• 2020

Smoking is one of the main causes of health problems and continues to be one of the world's most significant health challenges. In this paper, we use the multi-step Adomian decomposition method (MSADM) to obtain approximate analytical solutions for a mathematical fractional model of the evolution of the smoking habit. The proposed MSADM scheme is only a simple modification of the Adomian decomposition method (ADM), in which ADM is treated algorithmically with a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically. The results reveal that the method is effective and convenient for solving linear and nonlinear differential equations of fractional order.