• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.391-397
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• 2001

This paper explores the free vibrations of double hinged curved beams with transition segment. In this study, the clothoid curve is chosen as the transition segment of beams. The differential equations governing free vibration of such beams are derived in which the effects of rotatory inertia and shear deformation are included. The Runge-Kutta method and Determinant Search method are used to perform the integration of differential equations and to compute natural frequencies, respectively. In numerical examples, the double hinged end constraint is considered. The lowest four natural frequencies are presented as functions of three non-dimensional system parameters: the slenderness ratio, shear parameter and stiffness parameter.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.275-280
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• 2003

This paper discusses on the dynamic responsed of an elastically restrained beam under a moving mass of constant velocity. Governing equations of motion taking into account of all inertia effects of the moving mass were derived by Galerkin's mode summation method, and Runge-Kutta integration method was applied to solve the differential equations. Numerical solutions for dynamic deflections of beams were obtained for the changes of the various parameters (spring stiffness, spring position, mass ratios and velocity ratios of the moving mass). In order to verify the numerical predictions for the dynamic response of the beam, experiments were conducted. Numerical solutions for the dynamic responses of the test beam have a good agreement with experimental ones.

• Bulletin of the Society of Naval Architects of Korea
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• v.23 no.1
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• pp.3-12
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• 1986

This paper investigates the static configurations and the dynamic behaviors of a single point mooring line. To obtain the static configuration and static tension distribution along the mooring line, including the effect of fluid nonlinear drag and the elasticity of the line, the Runge-Kutta fourth order numerical method was used. The relationship between the horizontal excursion and the horizontal restoring force component of the mooring line, which is very important to a mooring line design, and the effect of a subsurface buoy on the static configuration are presented. In nonlinear dynamic analysis including nonlinear fluid drag acting on the line and geometrical nonlinearity for large deflections, finite element method using updated Lagrangian was used to obtain the solution. In the case of upper end harmonic excitation of the mooring line, the dynamic motion and the tension were also presented.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2003.10a
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• pp.59-62
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• 2003

We fabricated two HTS closed coils by using resistive-joint method and the joint resistance of the coil was estimated by field decay technique at 77 K. In addition, we used the Runge-kutta method for the numerical analysis to estimate the decay properties. The joint resistances were evaluated as a function of critical current of HTS closed coil and external field strength of excitation coil. It was observed that joint resistance was independent of critical current and external field strength. It was estimated that joint resistance was 8.0$\times$10$^{-9}$ $\Omega$ to 11.9$\times$10$^{-9}$ $\Omega$ for coils of contact length for 7 cm.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.19-26
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• 1996

The main purpose of this paper is to investigate a more accurate behavior analysis of tapered column with initial imperfection. The nonlinear differential equations governing the deflected shapes of the tapered column with initial imperfection are derived by large deflection theory and solved numerically using the Runge-Kutta method and Regula-Falsi method. Three kinds of cross-sectional shape with simply supported end constraint are considered in numerical examples. The load versus displacement curves including the left and right end rotations are presented in figures. The effect of cross-sectional shapes on deflected shape is analyzed, and the deflected shapes of column for several initial imperfections are shown in figure.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.151-156
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• 1996

The differential equations governing free, out of plane vibrations of horizontally curved beams are derived and solved numerically to obtain the natural frequencies and the mode shapes. The Runge-Kutta method and Regula-Falsi method are used to integrate the differential equations and to determine the natural frequencies, respectively. In nu- merical examples, the hinged-clamped end constraint is considered and four lowest frequency parameters are reported as functions of four non-dimensional system parameters: (1) opening angle, (2) slenderness ratio, (3) shear parameter and (4) stiffness parameter. Also, typical mode shapes of displacements and stress resultants are shown.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.341-348
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• 2000

The differential equations governing the free vibrations of stepped horizontally circular curved beams with circular cross-section are derived and solved numerically. In numerical method, the Runge-Kutta and Determinant Search methods are used for computing the natural frequencies and mode shapes. Frequencies and mode shapes are reported as the functions of non-dimensional system parameters. The numerical method developed herein for computing frequencies and mode shapes are efficient and reliable.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.11
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• pp.3031-3040
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• 1995

Two-dimensional incompressible Navier-Stokes equations have been solved by the node-centered finite volume method with the unstructured triangular meshes. The pressure-velocity coupling is handled by the artificial compressibility algorithm due to its computational efficiency associated with the hyperbolic nature of the resulting equations. The convective fluxes are obtained by the Roe's flux difference splitting scheme using edge-based connectivities and higher-order differences are achieved by a reconstruction procedure. The time integration is based on an explicit four-stage Runge-Kutta scheme. Numerical procedures with local time stepping and implicit residual smoothing have been implemented to accelerate the convergence for the steady-state solutions. Comparisons with experimental data and other numerical results have proven accuracy and efficiency of the present unstructured approach.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.115-122
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• 2002

The main purpose of this paper is to determine the static optimal shapes of tapered beams with constant volume. The linear, parabolic and sinusoidal tapers with the regular polygon cross-section are considered, whose material volume and span length are always held constant. The Runge-Kutta method is used to integrate the differential equation and also Shooting method is used to calculate the unknown boundary condition. Then the static optimal shapes are determined by reading the minimum values of the deflection versus section ratio curves plotted by the deflection data. In numerical examples, the various tapered beams are analyzed and those numerical results of this study are shown in figures.

• 유체기계공업학회:학술대회논문집
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• 1999.12a
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• pp.27-32
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• 1999

A numerical study based on the three-dimensional thin-layer Navier-Stokes solver is carried out to analyze the flowfield through a single stage transonic compressor. Explicit four-step Runge-Kutta scheme with spatially variable time step and implicit residual smoothing is used. The governing equations are discretized with exploit finite difference method. Mixed-out average method is used at the interface between rotor and stator. And, an artificial dissipation model is used to assure the stability of solution. The results with k-$\omega$ turbulence model were compared to the results with Baldwin-Lomax model, and physical phenomena of transonic compressor are presented. The two turbulence models give the results that show reasonably good agreements with experimental data.