• 한국해양공학회지
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• 제23권6호
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• pp.12-16
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• 2009

In this study, the wave profiles and kinematics of highly nonlinear waves at various water depths were calculated using a 2D fully nonlinear Numerical Wave Tank (NWT). The NWT was developed based on the Boundary Element Method (BEM) with the potential theory and the mixed Eulerian-Lagrangian (MEL) time marching scheme by 4th-order Runge-Kutta time integration. The spatial variation of intermediate-depth waves along the direction of wave propagation was caused by the unintended generation of 2nd-order free waves, which were originally investigated both theoretically and experimentally by Goda (1998). These free waves were induced by the mismatch between the linear motion of wave maker and nonlinear displacement of water particles adjacent to the maker. When the 2nd-order wave maker motion was applied, the spatial modulation of the waves caused by the free waves was not observed. The respective magnitudes of the nonlinear wave components for various water depths were compared. It was found that the high-order wave components greatly increase as the water depth decreases. The wave kinematics at various locations were calculated and compared with the linear and the Stokes 2nd-order theories.

• International Journal of Aeronautical and Space Sciences
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• 제14권3호
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• pp.201-209
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• 2013

Much numerical and experimental research has been done for the flow around an oscillating airfoil. The main research topics are vortex shedding, dynamic stall phenomenon, MAV's lift and thrust generation. Until now, researches mainly have been concentrated on analyzing the wake flow for the variation of frequency and amplitude at a low angle of attack. In this study, wake structures and acoustic wave propagation characteristics were studied for a plunging airfoil at high angle of attack. The governing equations are the Navier-Stokes equation with LES turbulence model. OHOC (Optimized High-Order Compact) scheme and 4th order Runge-Kutta method were used. The Mach number is 0.3, the Reynolds number is, and the angle of attack is from $20^{\circ}$ to $50^{\circ}$. The plunging frequency and the amplitude are from 0.05 to 0.15, and from 0.1 to 0.2, respectively. Due to the high resolution numerical method, wake vortex shedding and pressure wave propagation process, as well as the propagation characteristics of acoustic waves can be simulated. The results of frequency analysis show that the flow has the mixed characteristics of the forced plunging frequency and the vortex shedding frequency at high angle of attack.

• 한국전산유체공학회지
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• 제9권1호
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• pp.1-9
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• 2004

Large eddy simulation is used to investigate the compressible flow over a cavity with high aspect ratio. The sub-grid scale stresses are modeled using the dynamic model. The compressible Navier-Stokes equations are solved with the sixth order accurate compact finite difference scheme in the space and the 4th order Runge-Kutta scheme in the time. The buffer Bone techniques are used for non-reflecting boundary conditions. The results show the shear layer oscillation over the cavity. The votical disturbances, the roll-up of vorticity, and impingement and scattering of vorticity at the downstream cavity edge can be seen in the shear layer. Several peaks for the resonant frequencies are found in the spectra of the vertical velocity at the center-line. The most energetic Peak near the downstream edge is different from that at the center part of the cavity The pressure has its minimum value in the vortex core inside the cavity, and becomes very high at the downstream face of the cavity. The variation of the model coefficient predicted by the dynamic model is quite large between 0 and 0.3. The model coefficient increases in the stream-wise evolution of the shear layer and sharply decreases near the wall due to the wall effect.

• 한국해양공학회지
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• 제24권6호
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• pp.34-40
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• 2010

Bragg reflection of nonlinear waves is simulated by a 2D fully nonlinear numerical wave tank (NWT). The developed NWT was based on the Boundary Element Method (BEM) with potential theory and the mixed Eulerian-Lagrangian (MEL) time marching scheme with Runge-Kutta 4th-order time integration. A spatial variation of wave elevations and their Fourier amplitudes of each component are compared to investigate the effect of sea bottom ripples and their relative heights. The incident waves over an undulated sea bottom are partially reflected and changed to partial standing waves due to Bragg reflection. The present results are verified with linear calculations and experimental data. It is found that the 1st-order wave component is mainly affected by Bragg reflection and its spatial modulation is significant in front of the bottom ripples.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.169-174
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• 2003

The thermal design of the bus bar of a Gas-Insulated Switchgear(GIS) becomes important since the current-carrying capacity of the GIS is limited by maximum operating temperature. In order to predict temperature rise of the bus bar, a program has been developed. Various heat sources possibly generated in the bus bar are calculated in the program. To estimate temperature rises at the bus bar caused by the heat balance between the heat generation and heat transfer, the finite volume method as well as the $4^{th}$ order Runge-Kutta method has been employed. In the experiments, temperature rises at conductor, contact part and external tank are measured for full-scale gas-insulated bus bars. The comparisons of the predicted values of the heat balance calculation to those of the experiments are made. From the comparisons, it is concluded that the developed program can predict the temperature rise of the bus bar quite well.

• 한국기계가공학회지
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• 제13권6호
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• pp.88-98
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• 2014

A moving mass on a skewed linear guideway model to analyze the friction-induced stick-slip behavior of ball-screw-driven slides is proposed. To describe the friction force, a friction coefficient function is modelled as a third-order polynomial of the relative velocity between the slide mass and a guideway. A nonlinear differential equation of motion is derived and an approximate solution is obtained using a perturbation method for the amplitudes and base frequencies of both pure-slip and stick-slip oscillations. The results are presented with time responses, phase plots, and amplitude plots, which are compared adequately with those obtained by Runge Kutta 4th-order numerical integration, as long as the difference between the static and kinematic friction coefficients is small. However, errors in the results by the approximate solution increase and are not negligible if the difference between the friction coefficients exceeds approximately 40% of the static friction coefficient.

• International Journal of Aeronautical and Space Sciences
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• 제3권1호
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• pp.74-85
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• 2002

The numerical experiment has been conducted to investigate the unsteady shock wave reflecting phenomena. The cell-vertex finite-volume, Roe's upwind flux difference splitting method with unstructured grid is implemented to solve unsteady Euler equations. The $4^{th}$-order Runge-Kutta method is applied for time integration. A linear reconstruction of the flux vector using the least-square method is applied to obtain the $2^{nd}$-order accuracy for the spatial derivatives. For a better resolution of the shock wave and slipline, the dynamic grid adaptation technique is adopted. The new concept of grid adaptation technique, which is much simpler than that of conventional techniques, is introduced for the current study. Three error indicators (divergence and curl of velocity, and gradient of density) are used for the grid adaptation procedure. Considering the quality of the solution and the numerical efficiency, the grid adaptation procedure was updated up to $2^{nd}$ level at every 20 time steps. For the convenience of comparison with other experimental and analytical results, the case of interaction between the straight incoming shock wave and a sharp wedge is simulated for various flow conditions. The numerical results show good agreement with other experimental and analytical results, in the shock wave reflecting structure, slipline, and the trajectory of the triple points. Some critical cases show disagreement with the analytical results, but these cases also have been proven to show hysteresis phenomena.

• 한국전산유체공학회지
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• 제10권4호통권31호
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• pp.51-58
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• 2005

The unsteady supersonic flow over two- and three-dimensional cavities has been analyzed by the integration of unsteady Reynolds-Averaged Navier-Stokes(RANS) with the k-$\omega$ turbulence model. The unsteady flow is characterized by the periodicity due to the mutual relation between the shear layer and the internal flow in the cavity. An explicit 4th order Runge-Kutta scheme and an upwind TVD scheme based on the flux vector split with the van Leer limiters are used for time and space discritizations, respectively. The cavity has a L/D ratio of 3 for two-dimensional case, and same L/D and W/D ratio of I for three-dimensional case. The Mach and Reynolds numbers are 1.5 and 450000 respectively. In the three-dimensional flow, the field is observed to oscillate in the 'shear layer mode' with a feedback mechanism that follows Rossiter's formula. In the two-dimensional simulation, the self-sustained oscillating flow has more violent fluctuation inside the cavity. The primary fluctuating frequencies of two- and three- dimensional flow agree very well with the 2nd mode of Rossiter's frequency. In the three-dimensional flow, the 1st mode of frequency could be seen.

• 한국소음진동공학회논문집
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• 제22권9호
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• pp.879-888
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• 2012

This study aims to apply multistage homotopy perturbation method(MHPM) to space truss composed of discrete members to obtain a semi-analytical solution. For the purpose of this research, a nonlinear governing equation of the structures is formulated in consideration of geometrical nonlinearity, and homotopy equation is derived. The result of carrying out dynamic analysis on a simple model is compared to a numerical method of 4th order Runge-Kutta method(RK4), and the dynamic response by MHPM concurs with the numerical result. Besides, the displacement response and attractor in the phase space is able to delineate dynamic snapping properties under step excitations and the responses of damped system are reflected well the reduction effect of the displacement.

• Structural Engineering and Mechanics
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• 제89권1호
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• pp.33-46
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• 2024

The present research delves into the analysis of nonlinear free and forced vibrations of porous functionally graded (FG) shallow shells reinforced with oblique stiffeners, which are embedded in a nonlinear elastic foundation (NEF) subjected to external excitation. Two distinct types of PFG shallow shells, characterized by even and uneven porosity distribution along the thickness direction, are considered in the research. In order to model the stiffeners, Lekhnitskii's smeared stiffeners technique is implemented. With the stress function and first-order shear deformation theory (FSDT), the nonlinear model of the oblique stiffened shallow shells is established. The strain-displacement relationships for the system are derived via the FSDT and utilization of the von-Kármán's geometric assumptions. To discretize the nonlinear governing equations, the Galerkin method is employed. The model such developed allows analysis of the effects of the stiffeners with various angles as desired, in addition to the quantitative investigation on the influence of the surrounding nonlinear elastic foundations. To numerically solve the problem of vibrations, the 4th-order P-T method is used, as this method, known for its enhanced accuracy and reliability, proves to be an effective choice. The validation of the present research findings includes a comprehensive comparison with outcomes documented in existing literature. Additionally, a comparative analysis of the numerical results against those obtained using the 4th Runge-Kutta method is performed. The impact of stiffeners with varying angles and material parameters on the vibration characteristics of the present system is also explored. The researchers and engineers working in this field may use the results of this study as benchmarks in their design and research for the considered shell systems.