• KSCE Journal of Civil and Environmental Engineering Research
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• v.41 no.1
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• pp.39-48
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• 2021

In this paper, an analytical model is proposed for assessing the natural frequency of barrettes subjected to vertical loading. The differential equation governing the free vibration of rectangular friction piles embedded in inhomogeneous soil is derived. The governing equation is numerically integrated by Runge-Kutta technique and the eigenvalue of natural frequency is computed by Regula-Falsi method. The numerical solutions for the natural frequency of barrettes compare well with those obtained from finite element analysis. Illustrated examples show that the natural frequencies increase with an increase of the cross-sectional aspect ratio, the friction resistance ratio and the soil stiffness ratio, and decrease with an increase of the friction aspect ratio, the slenderness ratio and the load factor, respectively.

• Journal of Convergence for Information Technology
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• v.11 no.3
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• pp.132-139
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• 2021

The response characteristics of the forced vibration generated when the high-damped vehicle pass the bumped barrier was studied, and in particular, the response behavior of displacement, velocity and acceleration was analyzed for the forced vibration model. In addition, in order to obtain responses such as displacement, velocity, and acceleration, a numerical analysis technique of the Runge-Kutta-Gill method was performed in time domain. The response was successfully obtained in detail under several high damping conditions. As a numerical analysis result, the response of the vehicle was obtained by considering the vehicle body to which the impulse impact was applied. Also, the analysis result was compared with the experimental result in order to verify the validity of vehicle model. The amplitude and natural frequency of the vehicle were considered and analyzed. The Nyquist diagram of the vehicle model was also obtained and the relationship could be analyzed. And the vibration response was analyzed on different mass, damping and stiffness.

• Kyungpook Mathematical Journal
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• v.60 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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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.

• Proceedings of the KSME Conference
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• 2003.04a
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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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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• v.42 no.4
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.8
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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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• v.3 no.3
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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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• v.60 no.4
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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.