• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.1
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• pp.170-180
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• 1986

본 연구에서는 2자유도 Hamiltonian 운동계에서 비선형 정규모우드(normal mode)들의 안정성을 예측하기 위한 제3의 운동상수를 선형계의 진동수비가 1:1이고 포텐셜이 4차항까지 우함수인 일반계에 적용하여 발전시켰다. 이는 Hamiltonian을 정규모우드로 바꾸는 B-G변환과 함수들을 부호처리함과 Poincare map을 이용하다. 비선형계에서 비선형상수에 따라 모우드가 bifurcate되며, 각각의 모우드 안정성은 제3의 운동상수와 Poincare map으로 정확히 판정할 수 있다는 결론을 얻었다.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.879-889
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• 2003

This research deals with the nonlinearities of rocking vibration associated with impact and sliding on the rocking behavior of rigid block under two dimensional sinusoidal excitation which has different frequencies in two excitation direction. The varied excitation direction influences not only the rocking response but also the sliding motion and the rocking response shape. Chaotic responses are observed in wider excitation amplitude region, when the frequencies in each excitation direction are different. The complex behavior of chaotic response, in the phase space, is related with the trajectory of base excitation and sliding motion.

• 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.

• Journal of Broadcast Engineering
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• v.13 no.5
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• pp.677-680
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• 2008

In this paper, a new orthogonal frequency division multiplexing (OFDM) with 3-dimensional (3-D) signal mapper is proposed. Here, the signal mapper consists of signals on the surface of Poincare sphere. If the signal points are uniformly distributed and normalized to have the same average power, the minimum Euclidean distance of a 3-D constellation is much larger than that of a 2-D constellation. Computer simulation shows that the proposed OFDM has much improved error performance as compared with the conventional system.

• 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.

• Journal of Ocean Engineering and Technology
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• v.7 no.1
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• pp.13-24
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• 1993

The dispersion in the oscillatory flow generated by gravitational waves above the spatially periodic repples is studied. The steady parts of equations describing the orbit of the passive particle in a two dimensional field are assumed to be simply trigonometric functions. From the view point of nonlinear dynamics, the motion of the particle is chaotic under externally time-periodic perturbations which come from the wave motion. Two cases considered here are; (i) shallow water, and (ii) deep water approximation.