본 연구는 두점식 선박 계류시스템의 종방향 외력에 대한 비선형 동적거동 해석을 수행하였다. 특정 입력 매개변수에 대한 카오스 운동과 한계주기궤도 등의 비선형 거동의 특성을 연구하였다. 주로 비선형복원력은 계류시스템의 강한 비선형성과 동적거동의 다양성을 제공한다. 계의 운동방정식시뮬레이션에 사용된 수치 적분기는 4차 룽게쿠타법이다. 외력진폭과 주파수를 변화시킬 때 분기 그림과 동적불안정 현상들을 볼 수 있다. 외력의 주파수(진동수)가 0.4 rad/s인 경우 수많은 혼돈상태 점들 사이에 주기창이라 불리는 안정적인 주기해가 관측된다. 주파수가 0.7 rad/s인 경우는 외력진폭이 1.0을 초과할 때 혼돈 영역이 갑자기 증가한다. 주파수가 1.0 rad/s인 경우는 주파수가 0.4 rad/s 및 0.7 rad/s인 경우와 비교해 볼 때, 혼돈 운동이 약화된다. 아울러, 두점식 계류시스템은 각 매개변수에서 준주기 운동, 한계주기궤도, 대칭성의 깨짐과 같은 다양한 정상상태의 궤적이 관측된다.
본 연구는 두점식 선박 계류시스템의 종방향 외력에 대한 비선형 동적거동 해석을 수행하였다. 특정 입력 매개변수에 대한 카오스 운동과 한계주기궤도 등의 비선형 거동의 특성을 연구하였다. 주로 비선형복원력은 계류시스템의 강한 비선형성과 동적거동의 다양성을 제공한다. 계의 운동방정식 시뮬레이션에 사용된 수치 적분기는 4차 룽게쿠타법이다. 외력진폭과 주파수를 변화시킬 때 분기 그림과 동적불안정 현상들을 볼 수 있다. 외력의 주파수(진동수)가 0.4 rad/s인 경우 수많은 혼돈상태 점들 사이에 주기창이라 불리는 안정적인 주기해가 관측된다. 주파수가 0.7 rad/s인 경우는 외력진폭이 1.0을 초과할 때 혼돈 영역이 갑자기 증가한다. 주파수가 1.0 rad/s인 경우는 주파수가 0.4 rad/s 및 0.7 rad/s인 경우와 비교해 볼 때, 혼돈 운동이 약화된다. 아울러, 두점식 계류시스템은 각 매개변수에서 준주기 운동, 한계주기궤도, 대칭성의 깨짐과 같은 다양한 정상상태의 궤적이 관측된다.
This paper deals with the dynamical analysis of a two-point mooring vessel under surge excitations. The characteristics of nonlinear behaviors are investigated completely including bifurcation and limit cycle according to particular input parameter changes. The strong nonlinearity of the mooring sys...
This paper deals with the dynamical analysis of a two-point mooring vessel under surge excitations. The characteristics of nonlinear behaviors are investigated completely including bifurcation and limit cycle according to particular input parameter changes. The strong nonlinearity of the mooring system is mainly caused by linear and cubic terms of restoring force. The numerical simulation is performed based on the fourth order Runge-Kutta algorithm. The bifurcation diagram and several instability phenomena are observed clearly by varying amplitudes as well as frequencies of surge excitations. Stable periodic solutions, called the periodic windows, can be obtained in succession between chaotic clouds of dots in case of frequency ${\omega}=0.4rad/s$. In addition, the chaotic region is unexpectedly increased when external forcing amplitude exceeds 1.0 with the angular frequency of ${\omega}=0.7rad/s$. Compared to the cases for ${\omega}=0.4$, 0.7rad/s, the region of chaotic behavior becomes more fragile than in the case of ${\omega}=1.0rad/s$. Finally, various types of steady states including sub-harmonic motion, limit cycle, and symmetry breaking phenomenon are observed in the two-point mooring system at each parameter value.
This paper deals with the dynamical analysis of a two-point mooring vessel under surge excitations. The characteristics of nonlinear behaviors are investigated completely including bifurcation and limit cycle according to particular input parameter changes. The strong nonlinearity of the mooring system is mainly caused by linear and cubic terms of restoring force. The numerical simulation is performed based on the fourth order Runge-Kutta algorithm. The bifurcation diagram and several instability phenomena are observed clearly by varying amplitudes as well as frequencies of surge excitations. Stable periodic solutions, called the periodic windows, can be obtained in succession between chaotic clouds of dots in case of frequency ${\omega}=0.4rad/s$. In addition, the chaotic region is unexpectedly increased when external forcing amplitude exceeds 1.0 with the angular frequency of ${\omega}=0.7rad/s$. Compared to the cases for ${\omega}=0.4$, 0.7rad/s, the region of chaotic behavior becomes more fragile than in the case of ${\omega}=1.0rad/s$. Finally, various types of steady states including sub-harmonic motion, limit cycle, and symmetry breaking phenomenon are observed in the two-point mooring system at each parameter value.
* AI 자동 식별 결과로 적합하지 않은 문장이 있을 수 있으니, 이용에 유의하시기 바랍니다.
가설 설정
1) The vessel system exhibits complex dynamical behaviors such as periodic and chaotic responses. Stable periodic solutions, called the periodic windows, can be observed in succession between chaotic motion clouds of dots in case of ω = 0.
제안 방법
In this paper, we consider the two-point mooring system (with damped Duffing oscillator) in wave excitations and provide rich nonlinear behaviors, including limit cycles and chaotic oscillations.
이론/모형
Numerical simulations are conducted in MatlabTM, adopting as a control parameter with initial condition. The parameter values for vessel model are listed in Table 1.
성능/효과
2) Chaotic region is unexpectedly increased when external forcing amplitude exceeds 1.0 in case of ω = 0.7 rad/s.
후속연구
The test results are extremely helpful for understanding of nonlinear stability and bifurcation mechanism in mooring system. Finally, further research will be made to consider the mooring control synthesis for safety vessel operations.
참고문헌 (13)
Akhmet, M. U. and M. O. Fen(2012), Chaotic Period-Doubling and OGY Control for the Forced Duffing Equation, Journal of Communications in Nonlinear Science and Numerical Simulation, Vol. 17, pp. 1929-1946.
Banik, A. K. and T. K. Datta(2010), Stability Analysis of Two-Point Mooring System in Surge Oscillation, Journal of Computational and Nonlinear Dynamics, Vol. 5, pp. 1-8 (021005).
Belato, D., H. I. Weber, J. M. Balthazar and D. T. Mook(2001), Chaotic Vibrations of a Nonideal Electro-Mechanical System, Journal of Solids and Structures, Vol. 38, pp. 1699-1706.
Gottlieb, O.(1991), Nonlinear Oscillations, Bifurcations and Chaos in Ocean Mooring Systems, Doctoral Dissertation, Oregon State University, p. 28.
Gottlieb, O. and S. C. S. Yim(1992), Nonlinear Oscillations, Bifurcations and Chaos in a Multi-Point Mooring System with a Geometric Nonlinearity, Applied Ocean Research, Vol. 14, pp. 241-257.
Gottlieb, O. and S. C. S. Yim(1997), Nonlinear Dynamics of a Coupled Surge-Heave Small-Body Ocean Mooring System, Ocean Engineering, Vol. 24. No. 5, pp. 479-495.
King, P. E. and S. C. Yim(2007), Stochastic Control of Sensitive Nonlinear Motions of an Ocean Mooring System, Journal of Offshore Mechanics and Arctic Engineering, Vol. 129, pp. 29-38.
Mitra, R. K., A. K. Banik and S. Chatterjee(2017), State Feedback Control of Surge Oscillations of Two-Point Mooring System, Journal of Sound and Vibration, Vol. 386, pp. 1-20.
Ueda, Y.(1991), Survey of Regular and Chaotic Phenomena in the Forced Duffing Oscillator, Journal of Chaos, Solitons & Fractals, Vol. 1, No. 3, pp. 199-231.
Umar, A., T. K. Datta and S. Ahmad(2010), Complex Dynamics of Slack Mooring System Under Wave and Wind Excitations, The Open Oceanography Journal, Vol. 4, pp. 9-31.
Zou, K. and S. Nagarajaiah(2015), An Analytical Method for Analyzing Symmetry-Breaking Bifurcation and Period-Doubling Bifurcation, Journal of Communications in Nonlinear Science and Numerical Simulation, Vol. 22, pp. 780-792.
AI-Helper
※ AI-Helper는 부적절한 답변을 할 수 있습니다.