• The Transactions of the Korean Institute of Power Electronics
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• v.4 no.4
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• pp.368-376
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• 1999

This paper studies the operational characteristics of thyristor controlled shunt compensator in a simple power t transmission system. With Fourier series representation of the thyristor switching action and the system parameters, t the thyristor current equations are derived, which transmit the required real power of the simple power transmission s system. Bisection algorithm is used to solve the thyristor current equations, which informs the thyristor firing an밍e, t the thyristor conduction an밍e, the power flows and the harmonic characteristics. The stability analysis is performed w with the theory of Poincare mapping for the nonlinear discrete periodic dynamic system. EMTP simulations at the v various operating points show the transient characteristics of the thyristor controlled shunt compensator and C correspond to the results calculated with Fourier series representation and the stability analysis.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1922-1927
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• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• Journal of KSNVE
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• v.9 no.1
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• pp.196-205
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• 1999

The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.385-402
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• 2021

The geometry of Poincaré disk itself is interpreted without any mapping to different spaces. Our approach might be one of the shortest and is intended for educational contribution.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.799-804
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• 2001

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhotf-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.6
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• pp.75-85
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• 1994

주기함수의 외력을 갖는 버선형 시스템의 다양한 응답 특성을 구하기 위해 새로운 조화함수법(HBM)을 적용하였다. 새로운 조화함수법의 해는 비선형항을 선형항으로부터 따로 분리시킨 다음 같은 주파수 성분을 갖는 비선형 방정식들을 Newton-Raphosn법으로 풀어서 구하였다. 다양한 천이(Bifurcation) 특성을 해석적으로 판별하기 위하여 HBM의 해를 이용하여 구한 섭동 방정식의 Floquet 지수의 고유해를 사용하였다. 새로이 개발한 HBM과 천이 판별법을 1차원 비선형항을 갖는 구조물인 ALP(Articulated Loading Platform) 모델과 다차원인 비선 형 회전체 모델에 적용시켜 HBM의 해의 정확성과 이들 시스템의 천이 특성의 하나인 Chaos 존재를 확인 하였다.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.857-872
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• 1994

A PB-chain(Poincare-Birkhoff chain) is by definition a pair of elliptic and hyperbolic n-periodic orbits for a mapping and its existence has been well established numerically or analytically in many particular occasions such as in standard maps or twist maps [1, 8, 9] or Henon maps [1, 2, 12]. This paper gives focus on the investigaton of the appearance of such a PB-chain in a one-parameter family of general area-preserving maps and is in fact a generalization of the results given in [12] for a one-parameter family of specific area-preserving maps, so called Henon maps.

• The Korean Journal of Rheology
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• v.8 no.3_4
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• pp.187-198
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• 1996

최근에 본 연구자에 의해서 단축 스크류 공정에서 카오스 스크류라고 명명되어진 카오스 혼합장치가 성공적으로 개발되었다. 기하학적 조건이나 공정조건에 대한 설계변수로 카오스 스크류를 설계하기 위하여 체류시간, 포인카레 단면 그리고 혼합패턴등에 대한 계산 과 해석이 이루어져야 하는데 이를 단지 Runge-Kutta 방법에 의해 속도장을 적분한다면 상당한 계산시간이 소비된다. 이러한 수치문제를 극복하기 위하여 본논문에서는 새로운 사 상법을 제안한다. 이 방법으　 사용하면 벽면 근처의 특이점 영역에서도 수치문제가 해결된 다. 본 논문에서 제안하는 수치사상법은 Runge-Kutta 방법에 비하여 수치계산의 효율성과 정확도 면에서, 특히 유안요소법으로 얻은 속도장에 대하여 우수함이 밝혀졌다. 이러한 사상 법은 공간주기 유동장뿐만 아니라 시간주기 유동장에서 적용할수 있다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.9
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• pp.1711-1721
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• 1992

A nonlinear dissipative dynamical system can often have multiple attractors. In this case, it is important to study the global behavior of the system by determining the global domain of attraction of each attractor. In this paper we study the global behavior of a forced beam with two mode interaction. The governing equation of motion is reduced to two second-order nonlinear nonautonomous ordinary differential equations. When .omega. /=3.omega.$_{1}$ and .ohm.=.omega $_{1}$, the system can have two asymptotically stable steady-state periodic solutions, where .omega./ sub 1/, .omega.$_{2}$ and .ohm. denote natural frequencies of the first and second modes and the excitation frequency, respectively. Both solutions have the same period as the excitation period. Therefore each of them shows up as a period-1 solution in Poincare map. We show how interpolated mapping method can be used to determine the two four-dimensional domains of attraction of the two solutions in a very effective way. The results are compared with the ones obtained by direct numerical integration.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.11
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• pp.1410-1416
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• 1999

This paper aims at investigating the operating-mode characteristics of two-module Thyristor Controlled Series Compensator (TCSC) as an equivalent of the multi-module TCSC in a simple three-phase power transmission system. The load flow program is developed to analyze the steady-state characteristics of two-module TCSC system and to find the thyristor firing angles for the required real power flow. The stability calculation program is developed with Poincare mapping theory. Simulation studies of the TCSC power transmission system using EMTP are performed to evaluate the transient characteristics of two-module TCSC as a real power flow controller and to rpove the results of the load flow calculation and the stability analysis. In the process of the study, the operating-mode characteristics of two-module TCSC are evaluated and compared to those of single-module TCSC.