• Journal of Auto-vehicle Safety Association
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• v.5 no.1
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• pp.25-30
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• 2013

The main purpose of this research is to predict dynamic behavior of door locking system for side impact safety and the design process to avoid door opening is introduced. The equations of motion that represent the system are obtained from the energy equation. From them, the motion of door handle is predicted by using Runge-Kutta $4^{th}$ order method and the simulation result is compared with the real crash data. Also, the design guide to define the properties of door locking system from the standpoint of avoiding door opening phenomenon is introduced.

• Journal of the Korean Society of Combustion
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• v.1 no.2
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• pp.41-49
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• 1996

A numerical study is conducted to investigate the periodically unstable shock induced combustion around blunt bodies in stoichiometric hydrogen-air mixtures. Euler equations are spatially discretized by upwind-biased third order scheme and temporally integrated by Runge-Kutta method. Chemistry model used in this study involves 8 elementary kinetics steps and 7 species. At a constant Mach number, the effects of projectile size, inflow pressure and inflow temperature are examined with Lehr#s experimental condition as a reference. In addition to oscillation frequency, characteristic distances and time averaged values are found from the result to find an relation with dimensionless parameters. As a result, it is found that the effects of inflow pressure and body size are very similar and $Damk{\ddot{o}}hler$ number plays an important role in determining the instability characteristics.

• Proceedings of the KSR Conference
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• 2011.05a
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• pp.680-689
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• 2011

A dynamic analysis procedure is developed to provide a comprehensive estimation of the dynamic response spectrum for locomotive's wheels running over a Pre-Stressed Concrete (PSC) box girder bridge on the Korea high speed railway. The wheel force spectrum with the bridge behavior are analyzed as the dynamic procedure for various running speeds (50~450km/h). The high-speed railway locomotive (KTX) is used as 38-degree of freedom system. Three displacements(vertical, lateral, and longitudinal) and three rotational components (pitching, rolling, and yawing). For one car-body and two bogies as well as five movements except pitching rotation components for four wheel axes forces are considered in the 38-degree of freedom model. Three dimensional frame element is used to model of the PSC box girder bridges, simply supported span length of 40m. The irregulation of rail-way is derived using the exponential spectrum density function under assumption of twelve level tracks conditions based on the normal probability procedure. The dynamic responses of bridge passing through the railway locomotive with high-speed analyzed by Newmark-${\beta}$ method and Runge-Kutta method are compared and contrasted considering the developed models of bridge, track and locomotive comprehensively. The dynamic analyses of wheel forces by Runge-Kutta method which are able to analyze the forces with high frequency running on the bridge and ground rail-way are conducted. Additionally, wheel forces spectrum and three rotational components of vehicle body for three typical running speeds is also presented.

• Journal of the Korean Institute of Telematics and Electronics
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• v.19 no.6
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• pp.55-61
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• 1982

An analytic solution for the spectral response of linearly-chirped grating filter is derived, which takes the finite physical length of filter into account. In the usual case of broad-band linearly-chirped grating filter the analytic solution is expressed in terms of elementary functions, by approximating asymptotically the involved parabolic cylinder functions over different ranges of its argument. It is also shown that derived results are general enough to include previously-available approximations as particular cases, and that they agree well with the numerical solutions based upon the Runge-Kutta method.

• Steel and Composite Structures
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• v.14 no.1
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• pp.73-83
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• 2013

In this paper Hamiltonian Approach (HA) have been used to analysis the nonlinear free vibration of Simply-Supported (S-S) and for the Clamped-Clamped (C-C) Euler-Bernoulli beams fixed at one end subjected to the axial loads. First we used Galerkin's method to obtain an ordinary differential equation from the governing nonlinear partial differential equation. The effect of different parameter such as variation of amplitude to the obtained on the non-linear frequency is considered. Comparison of HA with Runge-Kutta 4th leads to highly accurate solutions. It is predicted that Hamiltonian Approach can be applied easily for nonlinear problems in engineering.

• Geomechanics and Engineering
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• v.16 no.4
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• pp.355-361
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• 2018

In this paper, nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation is studied. It has been tried to prepare a semi-analytical solution for whole domain of vibration. Only one iteration lead us to high accurate solution. The effects of linear elastic foundation on the response of the beam vibration are considered and studied. The effects of important parameters on the ratio of nonlinear to linear frequency of the system are studied. The results are compared with numerical solution using Runge-Kutta $4^{th}$ technique. It has been shown that the Max-Min approach can be easily extended in nonlinear partial differential equations.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• v.y2005m4
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• pp.343-346
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• 2005

Three dimensional structures of detonation wave propagating through a square-shaped duct were investigated using computational method and parallel processing. Inviscid fluid dynamics equations coupled with $variable-{\gamma}$ formulation and simplified one-step Arrhenius chemical reaction model were analysed by MUSCL-type TVD scheme and four stage Runge-Kutta time integration. The unsteady computational results in three dimension show the detailed mechanism of transverse mode and diagonal mode of detonation wave instabilities resulting same cell length but different cell width in smoked-foil record.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.4
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• pp.350-356
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• 1993

We carry out a numerical calculation to understand the nonlinear wave deformation around breakwaters using the Boussinesq equation, which is weakly nonlinear and weakly dispersive shallow water equation. A numerical method based on a finite element scheme and fourth order Runge-Kutta algorithm is employed to investigate the diffraction of incident waves by the breakwater. As a computational model, two-dimensional wave flume is treated. The breakwaters is perpendicular to the side wall of a channel. From the numerical results, the wave deformations according to the change of the length and the thickness of breakwaters are investigated. We also investigate the effect of the nonlinearity by comparing the results with the linear solutions.

• Journal of Astronomy and Space Sciences
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• v.5 no.1
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• pp.19-30
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• 1988

The existence of the j-type collision periodic orbit is examined on the condition of mass ratio 0.9878449 and Jacobian constant 2.9∼3.4. Using the Birckhoff's regularization method and the 5th order Runge-Kutta variable step-sized numerical roution introduced by Fehlberg (1968). we test their periodicities. As the results, 4 j-type collision orbits and 5 peculiar orbits are represented. There are good agreements in this collision orbits with the relationship between the period and the shape of orbit proposed by Pinotsis Zikides(1984).

• Journal of the Korea Computer Industry Society
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• v.5 no.3
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• pp.355-362
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• 2004

This paper presents the common and different results between the galloping cable and torsional oscillations in suspension bridge. Numerical results of the galloping cable and torsional oscillations in suspension bridge are presented by using the second-order Runge Kutta method under the initial conditions. This paper shows that large amplitude solution can coexist with the small amplitude one as the frequency and amplitude of the oscillation change. The differences in symmetry and transient effects are presented.