• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.312-315
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• 1993

Optimal control theories based on the maximum principles have been evolved and applied to distributed parameter systems(DPSs) represented by partial differential equations (PDEs) and integral equations (IEs). This paper intends to show that an optimal control of a tubular reactor described by a one-dimensional partial differential equation was obtained using the distributed parameter control method for parabolic PDEs. In develping an algorithm which implements the calculation, the method of lines (MOL) was adopted through using a package called the DSS/2. For the tubular reactor system chosen for this paper, the optimal control method based on PDEs with the numerical MOL showed to be more efficient than the one based on IEs.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.5
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• pp.101-107
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• 2001

This paper deals with the free vibrations of horizontally curved beams with mu1tiple elastic springs. Taking into account the effects of rotatory Inertia and shear deformation. differential equations governing the free vibrations of such beams are derived, In which each e1astic spring is modeled as a discrete Winkler foundation with very short longitudinal length. Differential equations are solved numerically to calculate natural frequencies and mode shapes. In numerical examples, the circular, Parabolic. sinusoidal and elliptic curved beams are considered. The parametric studies are conducted and the lowest four frequency parameters are reported In tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• Korean Journal of Hydrosciences
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• v.3
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• pp.61-79
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• 1992

In oder to predict the dispersion of a thermal discharge with strong turbulent and buoyant effects, the development of a numerical model using turbulence model and its application are significantly increased. In this study, a three-dimensional steady-state model for the surface discharge heated water into quiescent water body is developed. For the model closure of turbulent terms the four-equation turbulence model is used. For economic mumerical simulation, the elliptic governing equations are transformed to the partially parabolic equations. In general, the simulated results by the present model agree well with the experimental results by Pande and Rajratnam (1977). The model characteristics are presented in comparison with the predicted results from the two-eqauation turbulence model by McGuirk and Rodi (1979).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.875-880
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• 2001

This paper deals with the free vibrations curved beams with elastic springs. Taking into account the effects of rotatory inertia and shear deformation, differential equations governing the free vibrations of such beams are derived, in which each elastic spring is modeled as a discrete Winkler foundation with very short longitudinal length. Differential equations are solved numerically to calculate natural frequencies and mode shapes. In numerical examples, the circular, parabolic, sinusoidal and elliptic curved members are considered. The parametric studies are conducted and the lowest four frequency parameters are reported in tables and figures as the non-dimensional fonns. Also the typical mode shapes are presented.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.935-940
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• 2006

Numerical methods are developed for solving the elastica and buckling load of cantilever column with constant volume, subjected to a compressive end load. The linear, parabolic and sinusoidal tapers with the regular polygon cross-sections are considered, whose material volume and span length are always held constant. The differential equations governing the elastica of buckled column are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine the horizontal deflection at free end and the buckling load, respectively. The numerical methods developed herein for computing the elastica and the buckling loads of the columns are found to be efficient and reliable.

• Journal of the Korean Society of Industry Convergence
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• v.6 no.4
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• pp.307-313
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• 2003

A technique for the design of cooling tower fans with sweep is presented. This technique is developed using the equations for the one dimensional inviscid flow through the fan blade, the empirical equations, and the experimental correlations. A parabolic function is used to generate a sweep of the fan. Design data for the fan and the balde can be obtained for a given flow rate and a pressure rise. Also, the present method is used to construct the three dimensional model for the designed fan. Design data and the model show general characteristics of the axial propeller fan.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.887-892
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• 2003

A front-end cooling fan is designed and tested in the present study. The design technique is developed using the one-dimensional inviscid flow through the fan blade, the empirical equations, and the experimental correlations. Design data for the blade can be obtained for a given flow rate and a pressure rise. A parabolic function is used to generate a sweep of the fan. Characteristics of the blade geometry are discussed between the huh and the tip. The fan is tested in the fan test unit. The measured volume flow rate at the operating point is in good agreement with that of the design specifications. Sound pressure levels of the noise are predicted with the Ffowcs Williams-Hawkings equations. Calculation results of the sound pressure level(SPL) 1m away from the fan are obtained and cpmpared with the measured data.

• 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.43 no.5
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• pp.106-115
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• 2001

This paper deals with the free vibrations of horizontally curved beams partially supported on elastic foundations. Taking account of the effects of rotatory inertia and shear deformation, differential equations governing the free vibrations of such beams are derived, in which the Pasternak foundation model is considered as the elastic foundation. Differential equations are numerically solved to calculate natural frequencies and mode shapes. The experiments were performed in which the free vibration frequencies of such curved beams in laboratorial scale were measured and these results agreed quite well with the present studies. In numerical examples, the circular, parabolic, sinusoidal and elliptic curved members are considered. The parametric studies are performed and the lowest four frequency parameters are reported in tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.491-505
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• 2022

This paper is concerned with singularly perturbed convection-diffusion parabolic partial differential equations which have time-delayed. We used the Crank-Nicolson(CN) scheme to build a fitted operator to solve the problem. The underling method's stability is investigated, and it is found to be unconditionally stable. We have shown graphically the unstableness of CN-scheme without fitting factor. The order of convergence of the present method is shown to be second order both in space and time in relation to the perturbation parameter. The efficiency of the scheme is demonstrated using model examples and the proposed technique is more accurate than the standard CN-method and some methods available in the literature, according to the findings.