• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.941-958
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• 2000

Euler method is generalized to solve the system of nonlinear differential equations. The generalization is carried out by taking a special constant matrix S so that exp(tS) can be exactly computed. Such a matrix S is extracted from the Jacobian matrix of the given problem. Stability of the generalized Euler process is discussed. It is shown that the generalized Euler process is comparable to the fourth order Runge-Kutta method. We also exemplify that the important qualitative and geometric features of the underlying dynamical system can be recovered by the generalized Euler process.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.682-687
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• 2000

In this paper, the simulation methods using transmission lines are studied and realized, which are necessary in design and analysis of hydraulic control systems. The basic idea of this method is that system components are separated by transmission line element for simulation. The PI-controller can keep inductance level as low as desired. It can also handle nonlinearities and discontinuities without flag signal when restarting integration. Parallel hydraulic circuits are simulated using parallel processing algorithm. To shoe that using variable timestep size in each subsystem, simulation time can be reduced. Performance of the simulation results is compared with that of Runge Kutta method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.621-626
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• 1985

Unsteady groundwater flow in a three-layer unconfined aquifer has been studied theoretically and experimentally. Two different methods have been used in solving the governing equations of the flow, the nonlinear partial differential equations; (1) The governing equations are linearized for each layer and approximate solutions are obtained. (2) The governing equations are transformed to nonlinear ordinary differential equations, which are solved numerically by Runge-Kutta procedure. Fine, middle sized and coarse sands are used in the experiments. It is found that the solutions from the method(2) ( the reduction of partial differential equations to ordinary differential equations) give better agreement with the experimental results than the solution from the method(1).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.196-201
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• 2002

This paper deals with the active vibration control of a simply-supported beam under a Moving mass using fuzzy control technique. Governing equation3 for dynamic responses of the beam under a moving mass are derived by Galerkin's mode summation method. Dynamic responses of the beam are obtained by Runge-Kutta integration method, and are compared with experimental results. For the active vibration control of the beam due to moving mass, a controller based on fuzzy logic was designed. The numerical predictions for dynamic deflections of the beam have a good agreement with the experimental results well. As for the fuzzy control of the tested beam, more than 50% reductions of dynamic deflection and residual vibrations under a moving mass are demonstrated.

• Tribology and Lubricants
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• v.12 no.2
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• pp.65-73
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• 1996

Rapid increase of Refrigeration and Air conditioning system in modem industries brings attention to the urgency of core technology development in the area. This paper presents theoretical investigation of the lubrication characteristics of rotary compressor for refrigeration and air conditioning. In order to analyze the lubrication characteristics of the main & sub bearing of rotary compressor, the bearing force and locus of shaft center are analyzed by the dynamic analysis of rotary compressor and numerical analysis of Reynolds equation as the operating condition is changed in various ways. In this paper, we used the Runge-Kutta method for the dynamic analysis of rotary compressor and the SOR (Successive OverRelaxation) method for the numerical analysis of Reynolds equation. The result shows that the operating condition of sub bearing is severer than that of main bearing, and eccentricity ratio grows as the bearing force increases. It is believed that the result can be applied to the design of alternative refrigerant rotary compressor.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.10 s.115
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• pp.1074-1081
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• 2006

This paper deals with the dynamic stability analysis of clamped-hinged columns with constant volume. Numerical methods are developed for solving natural frequencies and buckling loads of such columns, subjected to an axial compressive load. The parabolic taper with the regular polygon cross-section is considered, whose material volume and column length are always held constant. Differential equations governing both free vibrations and buckled shapes of such columns are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine natural frequencies and buckling loads, respectively. The numerical methods developed herein for computing natural frequencies and buckling loads are found to be efficient and robust. From the numerical results, dynamic stability regions, dynamic optimal shapes and configurations of strongest columns are reported in figures and tables.

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.1
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• pp.57-65
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• 1992

The main purpose of this paper is to present both the natural frequencies and mode shapes of tapered beams under tensile axial force. The differential equation governing planar free vibration for tapered beams under tensile axial force is derived as nondimensional form. The three kinds of cross sectional shape are considered in differential equation. The Runge-Kutta method and 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, clamped-clamped and constraints are applied in numerical examples. The lowest four nondimensional natural frequencies are reported as the function of nondimensional tensile axial force. The fundamental natural frequencies are presented when section ratios and nondimensional axial forces are varied. The effects of cross sectional shapes are reported and some typical mode shapes are also presented.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.4
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• pp.17-23
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• 1998

This paper presents the motion of dynamically loaded journal in the connecting rod bearing of reciprocation internal combustion engine. Journal motions in engine bearings have been composed of two components, which was rotational and translational motion. Early study of journal locus in engine bearing had been performed on each motion. This paper has been considered two motions simultaneously. Reynolds equation including the squeeze effect has been analyzed using the ADI method, and real engine bearing and crankshaft system has been considered to calculate the cyclic external force. The equations are performed by 4th order Runge-Kutta method. This paper gives various journal orbits in connecting rod bearing depending on cyclic external forces, rotation speeds, and bearing parameters.

• Structural Engineering and Mechanics
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• v.3 no.5
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• pp.511-525
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• 1995

The differential equations governing in-plane free vibrations of the elastic, catenary arch with rotatory inertia are derived in Cartesian coordinates. Frequencies and mode shapes are computed numerically for such arches with unsymmetric axes, for both clamped-clamped and hinged-hinged end constraints. The lowest four natural frequency parameters are reported, with and without rotatory inertia, as a function of three nondimensional system parameters; the span to cord length ratio e, the slenderness ratio s, and the rise to cord length ratio f. Experimental measures of frequencies and mode shapes for several laboratory-scale catenary models serve to validate the theoretical results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.369-374
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• 2001

This paper deals with the buckling loads of column with rotation end restricted by rotational spring. The ordinary differential equations governing the buckling loads of such column is derived as nondimensional forms, and also its boundary conditions are derived. The buckled column model is based on the classical Bemoulli-Euler beam theory. The Runge-Kutta method and Regula-Falsi method are used to perform the integration of the differential equations and to determine the eigenvalue. The numerical methods developed herein for the buckling loads of the such column are found to be efficient and reliable. It is expected that the results obtained herein can be practically utilized in the structural engineering field.