• 한국안전학회지
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• 제14권2호
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• pp.42-51
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• 1999

This research deals with the non-linearities associated with impact and sliding for the rocking behavior of rigid block subjected to two dimensional excitation of horizontal and vertical direction. The non-linearities examined of impact between block and base: The transition of two governing rocking equations, the abrupt reduction in kinetic energy associated with impact. In this study, the rocking vibration system of two types are considered for several friction condition. One is the undamped rocking vibration system, disregarding energy dissipation at impact and the other is the damped rocking system, including energy dissipation at impact. The response analysis by non-dimensional rocking equation is carried out for the change of excitation amplitude. The chaos responses were discovered in the wide response region, particularly, in the case of high vertical excitation and their chaos characteristics are examined by Poincare map, power spectra and Lyapunov Exponent. The complex behavior of chaos response, in the phase space, were illustrated by Poincare map. Therefore, Poincare map will be a significant material in order to understand chaos of rocking system.

• 전산구조공학
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• 제10권4호
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• pp.251-265
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• 1997

해양계선시스템(offshore mooring system)의 거동을 구분적선형시스템(piecewise-linear system)을 이용하여 분석하였다. 계선시스템의 복원력을 유도하고 거기에 상응하는 근사치 구분적선형시스템의 복원력을 구하여 두 시스템의 복원력을 비교하였다. 다양한 파력 하에서의 계선시스템의 응답거동을 분석하였다. 시스템의 비선형정도 및 매개변수의 영향에 대하여 집중적으로 연구하였다. 시스템의 응답거동의 특성은 포인케어맵(Poincare map)을 통하여 확인하였다. 구분적선형시스템을 이용하여 분석한 결과, 계선시스템은 일반 조화, 열조화 및 복잡한 비선형거동인 chaos를 포함한 다양한 응답거동을 갖음을 알아냈다. 여러 값의 매개변수를 적용하여 시스템의 응답거동에 미치는 영향을 알아냈으며, 매개변수지도를 통하여 응답거동의 영역을 확인하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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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 Mechanical Science and Technology
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• 제16권9호
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• pp.1040-1053
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• 2002

This research deals with the influence of nonlinearities associated with impact and sliding upon the rocking behavior of a rigid block, which is subjected to two-dimensional horizontal and vertical excitation. Nonlinearities in the vibration were found to depend strongly on the effect of the impact between the block and the base, which involves an abrupt reduction in the system's kinetic energy. In particular, when sliding occurs, the rocking behavior is substantially changed. Response analysis using a non-dimensional rocking equation was carried out for a variety of excitation levels and excitation frequencies. The chaos responses were observed over a wide response region, particularly, in the cases of high vertical displacement and violent sliding motion, and the chaos characteristics appear in the time histories, Poincare maps, power spectra and Lyapunov exponents of the rocking responses. The complex behavior of chaotic response, in phase space, is illustrated by the Poincare map. The distribution of the rocking response is described by bifurcation diagrams and the effects of sliding motion are examined through the several rocking response examples.

• 한국정밀공학회지
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• 제12권1호
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• pp.123-131
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• 1995

다주파수 입력을 갖는 강한 비선형 시스템의 유사주기 (quasi-periodic) 해를 해석하기 위하여 개선된 고정 점법(FPA:Fixed Point Alogrithm)을 개발하였다. 안정성 및 천이 특성을 판별하기 위하여 사용되어지는 Floquest 지수인 해석적 자코비언을 구하기 위하여 Poincare 맵상에서 이산 적분법을 새로이 고안, 사용하였다. 본 방법의 우수성을 입증하기 위하여 2개의 주파수 입력을 갖는 선형 시스템과 비선형 시스템을 예로 사용하였다. 본 방법을 이용하여 비선형 시스템에서 발생한 복잡한 chaos 현상을 체계적으로 해석하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.441-448
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• 2000

An investigation into the nonlinear free vibrations of a cantilever beam which can have not only planar motion but also nonplanar motion is made. Using Galerkin's method based on the first mode in each motion, we transform the boundary and initial value problem into an initial value problem of two-degree-of-freedom system. The system turns out to have two normal modes. By Synge's stability concept we examine the stability of each mode. In order to check validity of the stability we obtain the numerical Poincare map of the motions neighboring on each mode.

• 소음진동
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• 제7권3호
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• pp.439-447
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• 1997

In this study, the dynamic instabilities of a nonlinear elastic system subjected to follower forces are investigated. The two-degree-of-freedom double pendulum model with nonlinear geometry, cubic spring, and linear viscous damping is used for the study. The constant, the initial impact forces acting at the end of the model are considered. The chaotic nature of the system is identified using the standard methods, such as time histories, power density spectrum, and Poincare maps. The responses are chaotic and unpredictable due to the sensitivity to initial conditions. The sensitivities to parameters, such as geometric initial imperfections, magnitude of follower force, direction control constant, and viscous damping, etc., are analysed. Dynamic buckling loads are computed for various parameters, where the loads are changed drastically for the small change of parameters.

• 대한수학회지
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• 제44권3호
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• pp.511-523
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• 2007

We consider a two parametric family of the planar systems with the form $\dot{x}=P(x,\;y)+{\in}_1p_1(x,\;y)+{\in}_2p_2(x,\;y)$, $\dot{y}=Q(x,\;y)+{\in}_1p_1(x,\;y)+{\in}_2p_2(x,\;y)$, where the unperturbed equation(${\in}_1={\in}_2=0$) is assumed to have at least one periodic solution or limit cycle. Our aim here is to study the behavior of the system under two parametric perturbations; in fact, using the Poincare-Andronov technique, we impose conditions on the system which guarantee persistence of the periodic trajectories. At the end, we apply the result on the Van der Pol equation ; where, we consider the effect of nonlinear damping on the equation. Also the Hopf bifurcation for the Van der Pol equation will be investigated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권3호
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• pp.179-199
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• 2018

The paper explores a tri-trophic food chain model with density dependent mortality of intermediate predator. To analyze this aspect, we have worked out the local stability of different equilibrium points. We have also derived the conditions for global stability of interior equilibrium point and conditions for persistence of model system. To observe the global behaviour of the system, we performed extensive numerical simulations. Our simulation results reveal that chaotic dynamics is produced for increasing value of half-saturation constant. We have also observed trajectory motions around different equilibrium points. It is noticed that chaotic dynamics has been controlled by increasing value of density dependent mortality parameter. So, we conclude that the density dependent mortality parameter can be used to control chaotic dynamics. We also applied basic tools of nonlinear dynamics such as Poincare section and Lyapunov exponent to investigate chaotic behaviour of the system.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 제14회 신호처리 합동 학술대회 논문집
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• pp.429-432
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• 2001

지문영상의 특이점(Singularities) 중의 하나인 Core Point는 대부분의 지문인증 시스템에서 기준점(Reference Point)으로 사용되고 있다. 또한 Core Point의 검출은 전체 지문인증 시스템의 가장 기본적인 단계로서 전체 시스템의 성능에 많은 영향을 준다. 본 논문에서는 지문 영상의 방향 패턴(Orientation Pattern)과 이의 리레이블링(Re-labeling)을 이용한 Core Point 검출 방법을 제안하고, 기존의 Poincare Index를 이용하는 방법 및 Sine Map을 이응한 방법과 비교, 분석하였다.