• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.215-219
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• 2003

Buckling and post-buckling Analysis of Ludwick type and modified Ludwick type elastic materials was carried out. Because the constitutive equation, or stress-strain relationship is different from that of linear elastic one, a new governing equation was derived and solved by $4^{th}$ order Runge-Kutta method. Considered as a special case of combined loading, the buckling under both point and distributed load was selected and researched. The final solution takes distinguished behavior whether the constitutive relation is chosen to be modified or non-modified Ludwick type as well as linear or non-linear. We also derived strain energy function for non-linear elastic constitutive relationship. By doing so, we calculated the criterion function which estimates the stability of the equilibrium solutions and determines critical buckling load for non-linear cases. We applied this theory to the constitutive relationship of fabric, which also is the non-linear equation between the applied moment and curvature. This results has both technical and mathematical significance.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.813-818
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• 2000

The objective of this study is to elucidate the characteristic performance of Roots-type vacuum pump with Cassini oval lobe shape. The modelled lobe shape of Roots-type vacuum pump is two-lobe spur gear. The numerical analyses are performed fer leak flows, using 4th-order Runge-Kutta method and are compared with experimental results. Results show that for the case of involute lobe shape the total amount of the leak flow conductance is greater than that of cycloid and Cassini oval lobe shapes.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.20 no.2
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• pp.121-127
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• 2008

This paper investigates the effects of outdoor pressure fluctuations on natural ventilation through an opening on a building envelope. The ventilation airflow rate depends on the magnitude and the period of the pressure fluctuations, the size of the opening relative to the space volume, and the resistance characteristics of the opening. Non-dimensional parameters have been derived, which determine indoor pressure responses due to outdoor pressure fluctuations. The flow regions are categorized into (1) synchronized region, (2) opening resistance region, and (3) transition region depending on the non-dimensional parameter derived. Pressure fluctuations and flow characteristics are investigated numerically using the 4th order Runge-Kutta method.

• Journal of Biomedical Engineering Research
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• v.13 no.3
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• pp.235-244
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• 1992

In this paper, fluttering behavior of mechanical monoleaflet tilting disc heart valve prostheses during the opening phase was analyzed taking into consideration the impact between the occluder and the guiding strut at the fully open position. The motion of the valve occluder was modeled as a rotating system, and equations were derived by employing the moment equilibrium principle. Forces due to lift, drag, gravity and buoyancy were considered as external forces acting on the occluder. The 4th order Runge-Kutta method was used to solve the governing equations. The results iimonstrated that the occludes reaches steady equilibrium position only after damped vibration. Fluttering frequency varies as a function of time after opening and is in the range of 8-84 Hz. Valve opening appears to be affected by the orientation of the valve relative to gravitational force. The opening velocities are in the range of 0.65-1.42m/sec and the dynamic loads by impact of the occludes and the strut are in the range of 90-190 N.

• Journal of Biomedical Engineering Research
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• v.12 no.3
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• pp.149-156
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• 1991

In this paper, fluttering behavior of mechanical bileaflet heart valve prosthesis was analyzed taking into consideration of the impact between valve plate and stopper Vibration system of the valve was modeled as a rotating system, and equations are induced by moment equilibrium equations. Lift force, drag force, gravity and buoyancy were considered as external forces acting on the valve plate/ The 4th order Runge-Kutta method was used to solve the equations. Valve plate does not come to the static equilibrium position at a stretch, but come to that position after under damping vibration. Damping ratio increases as the cardiac optput increases, and the mean damping ratio is in the range of 0.16~40.25. Fluttering frequency does not have any specific value, but varies as a function of time. It is in the range of 10~40Hz. Valve opening appears to be affected by the orientation of the of the valve relative to gravitational forces.

• Journal of Environmental Science International
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• v.6 no.4
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• pp.399-407
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• 1997

The pyrolysis reactions of atomic hydrogen with chloroform were studied In a 4 cm 1.6. tubular flow reactor with low flow velocity 1518 cm/sec and a 2.6 cm 1.4. tubular flow reactor with high flow velocity (1227 cm/sec). The hydrogen atom concentration was measured by chemiluminescence titration with nitrogen dioxide, and the chloroform concentrations were determined using a gas chromatography. The chloroform conversion efficiency depended on both the chloroform flow rate and linear flow velocity, but 416 not depend on the flow rate of hydrogen atom. A computer model was employed to estimate a rate constant for the initial reaction of atomic hydrogen with chloroform. The model consisted of a scheme for chloroform-hydrogen atom reaction, Runge-Kutta 4th-order method for Integration of first-order differential equations describing the time dependence of the concentrations of various chemical species, and Rosenbrock method for optimization to match model and experimental results. The scheme for chloroform-hydrogen atom reaction Included 22 elementary reactions. The rate constant estimated using the data obtained from the 2.6 cm 1.4. reactor was to be 8.1 $\times$ $10^{-14}$ $cm^3$/molecule-sec and 3.8 $\times$ $10^{-15}$ cms/molecule-sec, and the deviations of computer model from experimental results were 9% and 12% , for the each reaction time of 0.028 sec and 0.072 sec, respectively.

• Journal of Ocean Engineering and Technology
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• v.23 no.6
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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.

• Journal of Korean Society of Water and Wastewater
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• v.19 no.4
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• pp.487-496
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• 2005

Chlorine bulk decay tests were carried out by bottle test under controlled conditions in a laboratory. Experiments were performed at different temperatures: $5^{\circ}C$, $15^{\circ}C$, $25^{\circ}C$, and the water temperatures when samples were taken from the effluent just before entering to its distribution system. 38 bulk tests were performed for water of Al (water treatment plant), 4 bulk tests for A2 (large service reservoir), and A3(pumping station). Residual chlorine concentrations in the amber bottles were measured over time till about 100 hours and bulk decay coefficients were evaluated by assuming first-order, parallel first-order, second-order. and $n^{th}-order$ reaction. The $n^{th}-order$ coefficients were obtained using Fourth-order Runge-Kutta Method. A good-fit by the average coefficient of determination ($R^2$) was first-order ($R^2=0.90$) < parallel first-order ($R^2{_{fast}}=0.92$, $R^2{_{slow}}=0.95$) < second-order ($R^2=0.95$) < $n^{th}-order$ ($R^2=0.99$). But if fast reaction of parallel first-order bulk decay were applied to the effluent of large service reservoir with ca. 20 hours of travel time and slow reaction in the water distribution system following the first 20 hours, parallel first-order bulk decay would be best and easy for application of water quality modeling technique.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.9
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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.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.3
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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.