两栖车辆非线性横摇运动的Lyapunov特性指数分析
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摘要
为了确定两栖车辆在规则波浪激励下的非线性横摇运动形式,根据Lyapunov特性指数(LCE)的定义,采用QR分解法计算两栖车辆横摇运动的LCE,再根据计算出的LCE判断两栖车辆的运动形式.以两栖车辆为例,计算了当波浪频率与横摇固有频率的频率比为1时横摇运动为周期性的运动,当频率比为1.25时横摇运动为混沌运动,并通过数值仿真进行了验证.以频率比为控制变量,计算了当波浪扰动力矩一定时,两栖车辆在不同频率波浪激励下进入混沌运动的阈值.计算结果表明:利用LCE方法可以简单、准确地判断非线性横摇运动类型.
In order to determine the nonlinear rolling motion types of amphibious vehicle in regular waves,QR factorization method was applied to calculate Lyapunov characteristics exponents(LCE) according to the definition of LCE,and then the rolling motion types of amphibious vehicle could be judged by the obtained LCE.As an example,the LCE of the nonlinear rolling motion in regular wave of an amphibious vehicle were calculated in different frequency ratio between wave frequency and the nature frequency of rolling motion,respectively. When the frequency ratio R=1,the rolling motion is a period motion,and when the frequency ratio R=1.25,the rolling motion is a chaos motion.The obtained results are verified by numerical simulation results.Taking frequency as control variables,the LCE can be used to find the chaotic threshold of the amphibious vehicle nonlinear rolling motion in wave of different frequency at a constant disturbing moment of wave.The obtained result show the LCE is direct,concise and effective for judge the amphibious vehicle nonlinear rolling motion types.
In order to determine the nonlinear rolling motion types of amphibious vehicle in regular waves,QR factorization method was applied to calculate Lyapunov characteristics exponents(LCE) according to the definition of LCE,and then the rolling motion types of amphibious vehicle could be judged by the obtained LCE.As an example,the LCE of the nonlinear rolling motion in regular wave of an amphibious vehicle were calculated in different frequency ratio between wave frequency and the nature frequency of rolling motion,respectively. When the frequency ratio R=1,the rolling motion is a period motion,and when the frequency ratio R=1.25,the rolling motion is a chaos motion.The obtained results are verified by numerical simulation results.Taking frequency as control variables,the LCE can be used to find the chaotic threshold of the amphibious vehicle nonlinear rolling motion in wave of different frequency at a constant disturbing moment of wave.The obtained result show the LCE is direct,concise and effective for judge the amphibious vehicle nonlinear rolling motion types.
引文
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[19]马新谋,潘玉田,马昀.两栖作战武器线性横摇运动动力学分析[J].火炮发射与控制学报,2008(2):85-88.Ma Xinmou,Pan Yutian,Ma Yun.Linear roll motion dynamics analysis of amphibious combat weapon[J].Journalof Gun Launch&Control,2008(2):85-88.(in Chinese)
[20]徐国英,周景涛,姚新民,等.两栖车辆在波浪中的摇荡问题研究[J].兵工学报,2005,26(4):433-437.Xu Guoying,Zhou Jingtao,Yao Xinmin,et al.Toss motion of amphibious vehicle in sea-way[J].ActaArmamentarii,2005,26(4):433-437.(in Chinese)
[21]李远林,伍晓榕.非线性横摇阻尼的试验确定-数据处理方法[J].华南理工大学学报(自然科学版),2002,30(2):79-82.Li Yuanlin,Wu Xiaorong.Experimental determination of nonlinear roll damping:a technique for data processing[J].Journal of South China University of Technology(Natural Science Edition),2002,30(2):79-82.(in Chi-nese)
[22]Roberts J B.Estimation of nonlinear ship roll damping from free-decay data[J].Journal of Ship Research,1985,29(2):127-138.
[23]Chakrabarti S.Empirical calculation of roll damping for ships and barges[J].Ocean Engineering,2001,28:915-932.
[24]Rawson K J,Tupper E C.Basic Ship Theory(5thed)[M].Oxford,UK:Butterworth-Heinemann.A Division ofReed Educational and Professional Publishing Ltd.,2001:525-531.
[2]丁勇,胡开业,邱敏芝.船舶非线性横摇运动分析的Lyapunov特性指数法[J].中国造船,2008,49(3):1-6.Ding Yong,Hu Kaiye,Qiu Minzhi.The method of Lyapunov characteristic exponents for analyzing the stability ofship’s nonlinear rolling motion[J].Ship Building of China,2008,49(3):1-6.(in Chinese)
[3]袁远,余音,金咸定.船舶在规则横浪中的奇异倾覆[J].上海交通大学学报,2003,37(7):995-998.Yuan Yuan,Yu Yin,Jin Xianding.Undesirable ship capsizal in regular beam sea[J].Journal of Shanghai JiaotongUniversity,2003,37(7):995-998.(in Chinese)
[4]Taylan M.The effect of nonlinear damping and restoring in ship rolling[J].Ocean Engineering,2000,27:921-932.
[5]Nayfeh A H,Khdeir A A.Nonlinear rolling of ships in regular beam seas[J].International Shipbuilding Progress,1986,33(379):40-49.
[6]Wolf A,Swift J,Swinney H,et al.Determining Lyapunov exponents from a time series[J].Physica D,1985,16(9):302-310.
[7]Geist K,Parlit Z U,Lauterborn W.Comparison of different methods for computing Lyapunov exponents[J].Progress of Theoretical Physics,1990,83(5):875-893.
[8]Udwadia F E,Bremen HF.An efficient and stable approach for computation of Lyapunov characteristic exponents ofcontinuous dynamical systems[J].Applied Mathematics and Computation,2001,121:219-259.
[9]郑兆毖,张军,汪秉宏.最大Lyapunov指数计算的几种方法[J].地震,1994(4):86-92.Zheng Zhaobi,Zhang Jun,Wang Binghong.Several calculation methods of maximum Lyapunov exponent[J].Earthquake,1994(4):86-92.(in Chinese)
[10]何岱海,徐健学,陈永红.常微分方程系统李雅普诺夫特性指数的研究[J].物理学报,2000,49(5):833-837.He Daihai,Xu Jianxue,Chen Yonghong.Study on Lyapunov characteristic exponents of a nonlinear differentialequation system[J].Acta Physica Sinica,2000,49(5):833-837.(in Chinese)
[11]郁俊莉,王其文.Lyapunov指数混沌特性判定研究[J].武汉理工大学学报,2004,26(2):90-92.Yu Junli,Wang Qiwen.Research of Judging the chaotic characteristics with the Lyapunov exponents[J].Journal ofWuhan University of Technology,2004,26(2):90-92.(in Chinese)
[12]Christiansen F,Rugh H H.Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization[J].Nonlinearity,1997,10(5):1063-1072.
[13]Habib S,Ryne R D.Symplectic calculation of Lyapunov exponents[J].Physical Review Letters,1995:74(1):70-73.
[14]Rangarajan G,Habib S,Ryne R D.Lyapunov exponents without rescaling and reorthogonalization[J].PhysicalReview Letters,1998,80(17):3747-3750.
[15]Zeng X,Eykholt R,Pielke R A.Estimating the Lyapunov-exponent spectrum from short time series of lowprecision[J].Physical Review Letters,1991,66(25):3229-3242.
[16]Aurell E,Boffetta G,Crisanti A,et al.A vulpiani predictability in the large:an extension of the concept ofLyapunov Exponent[J].J.Phys.A:Math.Gen.,1997,30(1):1-26.
[17]Ginelli F,Poggi P,Turchi A,et al.Characterizing dynamics with covariant Lyapunov vectors[J].Physical ReviewLetters,2007,99(13):130601-130609.
[18]刘延柱,陈立群.非线性振动[M].北京:高等教育出版社,2001:266-270.
[19]马新谋,潘玉田,马昀.两栖作战武器线性横摇运动动力学分析[J].火炮发射与控制学报,2008(2):85-88.Ma Xinmou,Pan Yutian,Ma Yun.Linear roll motion dynamics analysis of amphibious combat weapon[J].Journalof Gun Launch&Control,2008(2):85-88.(in Chinese)
[20]徐国英,周景涛,姚新民,等.两栖车辆在波浪中的摇荡问题研究[J].兵工学报,2005,26(4):433-437.Xu Guoying,Zhou Jingtao,Yao Xinmin,et al.Toss motion of amphibious vehicle in sea-way[J].ActaArmamentarii,2005,26(4):433-437.(in Chinese)
[21]李远林,伍晓榕.非线性横摇阻尼的试验确定-数据处理方法[J].华南理工大学学报(自然科学版),2002,30(2):79-82.Li Yuanlin,Wu Xiaorong.Experimental determination of nonlinear roll damping:a technique for data processing[J].Journal of South China University of Technology(Natural Science Edition),2002,30(2):79-82.(in Chi-nese)
[22]Roberts J B.Estimation of nonlinear ship roll damping from free-decay data[J].Journal of Ship Research,1985,29(2):127-138.
[23]Chakrabarti S.Empirical calculation of roll damping for ships and barges[J].Ocean Engineering,2001,28:915-932.
[24]Rawson K J,Tupper E C.Basic Ship Theory(5thed)[M].Oxford,UK:Butterworth-Heinemann.A Division ofReed Educational and Professional Publishing Ltd.,2001:525-531.
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