• Journal of KSNVE
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• v.6 no.2
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• pp.233-244
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• 1996

In this paper chaotic mothions of a straight pipe conveying oscillatory flow and being subjected to external forces such as earthquake are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. In this equation, the nonlinear curvature of the pipe and the thermal expansion effects are contained. The nonlinear ordinary differential equation transformed from that partial differential equation is a type of Hill's equations, which have the parametric and external exciation term. This original system is transfered to the averaged system by the averaging theory. Bifurcation curves of chaotic motion of the piping system are obtained in the general case of the frequency ratio, n by applying Melnikov's method. Numerical simulations are performed to demonstrate theorectical results and show strange attactors of the chaotic motion.

• Journal of information and communication convergence engineering
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• v.2 no.3
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• pp.187-192
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• 2004

A method using two dimension Haar functions approximation for solving the problem of a partial differential equation and estimating the parameters of a non-linear distributed parameter system (DPS) is presented. The applications of orthogonal functions, including Haar functions, and their transforms have been given much attention in system control and communication engineering field since 1970's. The Haar functions set forms a complete set of orthogonal rectangular functions similar in several respects to the Walsh functions. The algorithm adopted in this paper is that of estimating the parameters of non-linear DPS by converting and transforming a partial differential equation into a simple algebraic equation. Two dimension Haar functions approximation method is introduced newly to represent and solve a partial differential equation. The proposed method is supported by numerical examples for demonstration the fast, convenient capabilities of the method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.11
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• pp.2023-2026
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• 2007

In this letter, the problem for a class of neutral differential equation is considered. Based on the Lyapunov method, a stability criterion, which is delay-dependent on both ${\tau}\;and\;{\sigma}$, is derived in terms of linear matrix inequality (LMI). Two numerical examples are carried out to support the effectiveness of the proposed method.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.91-106
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• 1997

The existence and the smoothness of density of random variables which are solutions of the canonical stochastic differential equation can be proved by simpler conditions in the Malliavin-Bismut method.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.199-209
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• 1997

The existence and the smoothness of densities of random variables, which are generated by the canonical stochastic differential equation, can be proved by the Malliavin - Bismut method.

• Korean Journal of Mathematics
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• v.8 no.1
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• pp.1-17
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• 2000

The existence of density of process, which is given by canonical stochastic differential equation, can be proved by the Picard's method([5]) also.

• Journal of KSNVE
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• v.7 no.3
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• pp.489-498
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• 1997

In this paper, chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonliear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which has the external and parametric excitation with a same frequency. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Numerical simulations are performed to demonstrate theoretical results and show the strange attractor of the chaotic motion.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.957-962
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• 2004

This paper deals with the free vibration analysis of beam-columns resting on Pasternak foundation by the Differential Quadrature Method. Based on the differential equation subjected to the boundary conditions, adopted from the open literature, which governs the free vibrations of such member, this equation is applied to the Differential Quadrature Method. For computing natural frequencies, the numerical procedures are developed by QR Algorithm, in which the Chebyshev-Gauss-Lobatto method is used for choosing the grid points. The numerical methods developed herein for computing natural frequencies are programmed in FORTRAN code, and all solutions obtained in this study are quite agreed with those in the open literature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.253-266
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• 2019

In this article, a systematic solution based on the sequence of expansion method is planned to solve the time-fractional diffusion equation, time-fractional telegraphic equation and time-fractional wave equation in three dimensions using a current and valid approximate method, namely the ADM, VIM, and the NIM subject to the estimate initial condition. By using these three methods it is likely to find the exact solutions or a nearby approximate solution of fractional partial differential equations. The exactness, efficiency, and convergence of the method are demonstrated through the three numerical examples.

• Structural Engineering and Mechanics
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• v.12 no.1
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• pp.85-100
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• 2001

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.