• Journal of the Earthquake Engineering Society of Korea
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• v.5 no.5
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• pp.25-33
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• 2001

For the seismic design and analysis of LMR(liquid metal reactor) being developed in Korea, it is necessary to develop the simple seismic analysis model including the fluid-structure interaction effects. In this paper, the theoretical backgrounds for the fluid added mass of the immersed concentric cylinders are investigated and the seismic analysis code using the Runge-Kutta algorithm, which can consider the fluid added mass matrix in system matrix, are developed to perform the time history seismic analysis. Form the coupled modal analysis and the seismic analysis for the simple immersed concentric cylinders, it is verified that the fluid added mass significantly affect the vibration characteristics and the seismic responses. Therefore the fluid coupled effects should be carefully considered in seismic response analysis of the immersed concentric cylinders.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.3
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• pp.37-46
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• 1991

A method is developed for solving the natural frequencies and mode shapes of linearly variable tapered beams. The governing differential equation for the tapered beam is derived. Three kinds of cross sectional shape are considered in differential equation. The Runge-Kutta method and the determinant search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped, damped-clamped and free-damped end constraints are investigated in numerical examples. The lowest four nondimensional natural frequencies are obtained as functions of $d_b/d_a$. ratio. The effects of end constraints and cross sectional shapes on frequencies are analyzed and typical mode shapes are also presented.

• Journal of KSNVE
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• v.10 no.6
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• pp.1067-1074
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• 2000

Numerical methods for calculating both the natural frequencies and buckling loads of columns with the multiple elastic springs are developed. In order to derive the governing equations of such columns, each elastic spring is modeled as a discrete elastic foundation with the finite longitudinal length. By using this model, the differential equations governing both the free vibrations and buckled shapes, respectively, of such columns are derided. These differential equations are solved numerically. The Runge- Kutta method is used to integrate the differential equations, and the determinant search method combined with Regula-Falsi method is used to determine the eingenvalues. namely natural frequencies and buckling loads. In the numerical examples, the clamped-clamped. clamped-hinged, hinged-clamped and hinged-hinged end constraints are considered. Extensive numerical results including the frequency parameters, mode shapes of free vibrations and buckling load parameters are presented in the non-dimensional forms.

• 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.

• Journal of the Korean Society of Combustion
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• v.13 no.1
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• pp.17-22
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• 2008

A partly implicit/quasi-explicit method is introduced for the solution of detailed chemical kinetics with stiff source terms based on the standard fourth-order Runge-Kutta scheme. Present method solves implicitly only the stiff reaction rate equations, whereas the others explicitly. The stiff equations are selected based on the survey of the chemical Jaconian matrix and its Eigenvalues. As an application of the present method constant pressure combustion was analyzed by a detailed mechanism of hydrogen-air combustion with NOx chemistry. The sensitivity analysis reveals that only the 4 species in NOx chemistry has strong stiffness and should be solved implicitly among the 13 species. The implicit solution of the 4 species successfully predicts the entire process with same accuracy and efficiency at half the price.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.4 s.235
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• pp.578-583
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• 2005

This paper introduces a fast Fourier transform (FFT)-based spectral dynamic analysis method for the transient responses as well as the steady-state responses of the linear discrete systems subject to non-zero initial conditions. The forced vibration of a viscously damped three-DOF system is considered as the illustrative numerical example. The proposed spectral analysis method is evaluated by comparing its results with the exact analytical solutions and the numerical solutions obtained by the Runge-Kutta method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.2
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• pp.445-451
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• 1993

For the calculation of transonic laminar flow fields in cascades of turbomachinery, a finite volume method employing Jameson's Runge-Kutta integration scheme as a basic algorithm is presented. The cell-vertex scheme introducing half-spacing mesh cells is developed. For the velocity gradients in the stress terms the integration with divergence theorem is used for the average concept. Some numerical results show good agreement with experimental data.

• Journal of computational fluids engineering
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• v.15 no.4
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• pp.76-84
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• 2010

In order to analyze the periodic unsteady flow problem efficiently the partially implicit harmonic balance (PIHB) method was developed. Contrary to the existing harmonic balance method, this method handles the harmonic source term explicitly and deals with flux terms implicitly. This method has a good convergence in comparison with the full explicit harmonic method and it is easy to apply this method because there is no need to calculate the complicated flux Jacobian term by comparing with the full implicit harmonic method. With the multigrid method about the each harmonic it turns out that this method has a good convergence regardless of the number of harmonics. The oscillating flows over NACA0012 airfoil is considered to verify this method then the result correponsed to both the result of dual time stepping and explicit Runge-Kutta method.

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.5
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• pp.112-122
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• 1999

이 논문은 일정체적을 갖는 양단고정 변단면 기둥의 좌굴하중 및 후좌굴 거동에 관한 연구이다. 기둥의 변단면으로는 직선형, 포물선형, 정현의 선형을 갖는세 가지 변단면을 채택하였다. Bernoulli-Euler 보 이론을 이용하여 압축하중이 작용하여 좌굴된 기둥이 정확탄성곡선을 지배하는 미분방정식을 유도하였다. 유도된 미분방정식을 Runge-Kutta 법과 REgula-Falsi법을 이용하여 수치해석하였다. 수치해석의 결과로 좌굴하중, 좌굴기둥의 평형경로 및 정확탄성곡선을 산출하였다. 또한 좌굴하중-단면비 곡선으로부터 최강기둥의 좌굴하중과 단면비를 산출하였다.

• Journal of the Korean Society for Railway
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• v.9 no.1 s.32
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• pp.63-68
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• 2006

This paper proposes a fast Fourier transform(FFT)-based spectral analysis method(SAM) for the dynamic responses of the linear discrete dynamic models with non-proportional damping. The SAM was developed by using discrete Fourier transform(DFT)-theory. To verify the proposed SAM, a three-DOF system with non-proportional viscous damping is considered as an illustrative example. The present SAM is evaluated by comparing the dynamic responses obtained by SAM with those obtained by Runge-Kutta method.