船舶在波浪中的大幅横摇运动及其运动稳定性研究
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摘要
船舶的航行安全性是船舶设计和使用人员最为关注的问题之一，为了揭示船舶在波浪中倾覆的力学机理，保障船舶的航行安全性，本文采用非线性动力学方法分析了船舶在波浪中的非线性横摇运动及其运动稳定性，提出了提高船舶在波浪中运动稳定性的措施。本文的主要工作和成果有：
总结了船舶大幅横摇运动中存在的非线性因素及其不同表达式的优缺点，分析了非线性系数的计算方法，针对恢复力矩项，提出了一种快速获得非线性恢复力矩系数的公式法。在此基础上，建立了船舶在正横规则波作用下的非线性横摇运动方程。
采用多尺度法研究了船舶在波浪中发生主共振、超谐共振和亚谐共振时的非线性横摇运动,给出上述共振情况下的近似解析解，利用久期项条件分析其幅频响应特性。采用数值方法验证了近似解析解的有效性。
应用时历图、相图、庞加莱截面图等多种混沌识别方法对船舶在波浪中横摇运动的稳定性进行了判断，分析比较了各种方法的优缺点，指出分岔和混沌是导致船舶倾覆的重要原因之一。为了避免对船舶的运动状态作出错误的评估，论文采用了一种高效的Lyapunov指数算法计算了船舶非线性横摇运动系统的Lyapunov指数，并利用该方法精确确定出了船舶横摇运动出现混沌态时的外激励阈值。
采用Melnikov方法对船舶横摇运动稳定域作了解析预测。针对传统计算Melnikov函数解析方法的不足，提出了一种计算Melnikov函数的数值积分方法，并利用该数值积分方法计算了非线性项较为复杂、无法采用解析方法计算的船舶非线性横摇运动系统产生不稳定横摇运动的波浪力阈值，采用安全池法对数值积分法的计算结果进行了验证。
为了提高船舶在正横规则波中横摇运动的稳定性，作者根据分岔理论设计了多种分岔控制器，通过分析，给出了各分岔控制器控制参数取值的建议，通过引入本文所设计的分岔控制器，可以消除或延缓分岔的产生，以提高船舶横摇运动的稳定性。
利用Lyapunov指数法对船舶在纵浪中发生参数激励横摇运动的稳定性进行了分析，得到了船舶在纵浪中航行时的安全域与不安全域。为了提高船舶在纵浪中横摇运动的稳定性，作者设计一分岔控制器，通过数值仿真表明，本文所设计的分岔控制器在适当的控制策略下可以提高船舶在纵浪中的横摇运动稳定性。
采应用马尔科夫扩散过程理论分析了船舶在随机横浪中横摇运动概率响应，提出了采用有限差分法结合超松弛迭代法计算船舶非线性随机横摇系统所对应的FPK方程。针对马尔科夫扩散过程方法需要将波浪外激励简化为白噪声这一不足，提出将波浪激励近似处理为有界噪声的方法，并利用随机Melnikov方法得到了船舶在随机纵浪中的全局稳定性。对于船舶在随机纵浪中的横摇运动，提出将随机参数激励项考虑为一窄带随机过程，推导得出了该非线性随机动力学系统的最大Lyapunov指数和稳态概率密度的表达式，由此得出了船舶在随机纵浪中的稳定性。
Ship navigation on the sea safety is one of issues that ship designers and user willconcern most. In order to reveal the mechanism of ship capsize, this dissertation use nonlineardynamics methods to analysis the ship nonlinear rolling movement and stability on the seas.The main work and conclusions of this dissertation are as follow:
Summarized the nonlinear factors that exist in ship’s large amplitude rolling, analyzedthe methods to calculate the nonlinear terms. Proposed a method that can calculate thenonlinear coefficients of restoring moment of ships rapidly. Established the nonlinear rollingequation of ships on regular beam seas.
The multiscale method is used to study the main, ultraharmonic and subharmonicresonances of nonlinear rolling in regular beam seas, and the approximate solutions of thethree resonances were given. At the same time, the characteristics of the threefrequency-amplitude responses were analyzed depending on the secular terms. Thepertubation solutions are compared with solutions obtained by numerical intergration of thenonlinear governing roll equation and the results show that the approximate analysis solutionsare valid.
Use different of chaos identification methods to determine the stability of ship in thebeam wave. Analyze and compare the advantages and disadvantages of different methods andindicate bifurcation and chaos will lead to ship capsize. A fast and efficient algorithm forcompute Lyapunov exponents is applied to ship’s nonlinear rolling system. The results showthat this method can judge the state of ship’s nonlinear rolling system accurately.
The Melnikov method was used to study the ship’s nonlinear rolling differential equation,a numerical method was presented to compute the melnikov function, and to get the curve ofthreshold above which chaos may occur, the result are validate by safe basin method.
In order to increase the stability region of ship in regular beam wave, a feedback controllaw is designed to control the bifurcations taking place in the resonance response, thusremoving or delaying the occurrence of jump and hysteresis phenomena. Numericalsimulations are performed to verify the effectiveness of the proposed feedback control.
The stability regions of ship in longitudinal wave are analyzed by the Lyapunov exponents method. A feedback control law is designed to improve the stability of ship inlongitudinal wave, numerical simulations are performed to verify the effectiveness of theproposed feedback control.
The combination of the finite difference method and the successive over relaxationmethod is employed to numerically solve the stationary solutions of FPK equation of ship’snonlinear rolling system． The joint probability density function and stationary meanout-crossing rate are investigated for ship nonlinear rolling subjected to additive white noiseexcitation.
Basing on the nonlinear dynamics theory, the global stability of ship in stochastic beamsea is researched by the global bifurcation method. Considered the stochastic excitation termas bounded noise and the influence of nonlinear damping and nonlinear righting moment, therandom single degree of freedom nonlinear rolling equation is established. The randomMelnikov mean-square criterion is used to analysis the global stability of this system. Theship’s prarmetrical rolling equation in stochastic longitudinal waves is established, theprincipal resonance of the paramerically excited system is investigated. The method ofmultiple scales was used to determine the equations of modulation of amplitude and phase.The stability and steady state response were studied. The influence of ship’s damping, themain frequences of the stochastic wave and the bandwidth of the waves for the ship’s saftyregin in longitudinal waves are analyzed.
总结了船舶大幅横摇运动中存在的非线性因素及其不同表达式的优缺点，分析了非线性系数的计算方法，针对恢复力矩项，提出了一种快速获得非线性恢复力矩系数的公式法。在此基础上，建立了船舶在正横规则波作用下的非线性横摇运动方程。
采用多尺度法研究了船舶在波浪中发生主共振、超谐共振和亚谐共振时的非线性横摇运动,给出上述共振情况下的近似解析解，利用久期项条件分析其幅频响应特性。采用数值方法验证了近似解析解的有效性。
应用时历图、相图、庞加莱截面图等多种混沌识别方法对船舶在波浪中横摇运动的稳定性进行了判断，分析比较了各种方法的优缺点，指出分岔和混沌是导致船舶倾覆的重要原因之一。为了避免对船舶的运动状态作出错误的评估，论文采用了一种高效的Lyapunov指数算法计算了船舶非线性横摇运动系统的Lyapunov指数，并利用该方法精确确定出了船舶横摇运动出现混沌态时的外激励阈值。
采用Melnikov方法对船舶横摇运动稳定域作了解析预测。针对传统计算Melnikov函数解析方法的不足，提出了一种计算Melnikov函数的数值积分方法，并利用该数值积分方法计算了非线性项较为复杂、无法采用解析方法计算的船舶非线性横摇运动系统产生不稳定横摇运动的波浪力阈值，采用安全池法对数值积分法的计算结果进行了验证。
为了提高船舶在正横规则波中横摇运动的稳定性，作者根据分岔理论设计了多种分岔控制器，通过分析，给出了各分岔控制器控制参数取值的建议，通过引入本文所设计的分岔控制器，可以消除或延缓分岔的产生，以提高船舶横摇运动的稳定性。
利用Lyapunov指数法对船舶在纵浪中发生参数激励横摇运动的稳定性进行了分析，得到了船舶在纵浪中航行时的安全域与不安全域。为了提高船舶在纵浪中横摇运动的稳定性，作者设计一分岔控制器，通过数值仿真表明，本文所设计的分岔控制器在适当的控制策略下可以提高船舶在纵浪中的横摇运动稳定性。
采应用马尔科夫扩散过程理论分析了船舶在随机横浪中横摇运动概率响应，提出了采用有限差分法结合超松弛迭代法计算船舶非线性随机横摇系统所对应的FPK方程。针对马尔科夫扩散过程方法需要将波浪外激励简化为白噪声这一不足，提出将波浪激励近似处理为有界噪声的方法，并利用随机Melnikov方法得到了船舶在随机纵浪中的全局稳定性。对于船舶在随机纵浪中的横摇运动，提出将随机参数激励项考虑为一窄带随机过程，推导得出了该非线性随机动力学系统的最大Lyapunov指数和稳态概率密度的表达式，由此得出了船舶在随机纵浪中的稳定性。
Ship navigation on the sea safety is one of issues that ship designers and user willconcern most. In order to reveal the mechanism of ship capsize, this dissertation use nonlineardynamics methods to analysis the ship nonlinear rolling movement and stability on the seas.The main work and conclusions of this dissertation are as follow:
Summarized the nonlinear factors that exist in ship’s large amplitude rolling, analyzedthe methods to calculate the nonlinear terms. Proposed a method that can calculate thenonlinear coefficients of restoring moment of ships rapidly. Established the nonlinear rollingequation of ships on regular beam seas.
The multiscale method is used to study the main, ultraharmonic and subharmonicresonances of nonlinear rolling in regular beam seas, and the approximate solutions of thethree resonances were given. At the same time, the characteristics of the threefrequency-amplitude responses were analyzed depending on the secular terms. Thepertubation solutions are compared with solutions obtained by numerical intergration of thenonlinear governing roll equation and the results show that the approximate analysis solutionsare valid.
Use different of chaos identification methods to determine the stability of ship in thebeam wave. Analyze and compare the advantages and disadvantages of different methods andindicate bifurcation and chaos will lead to ship capsize. A fast and efficient algorithm forcompute Lyapunov exponents is applied to ship’s nonlinear rolling system. The results showthat this method can judge the state of ship’s nonlinear rolling system accurately.
The Melnikov method was used to study the ship’s nonlinear rolling differential equation,a numerical method was presented to compute the melnikov function, and to get the curve ofthreshold above which chaos may occur, the result are validate by safe basin method.
In order to increase the stability region of ship in regular beam wave, a feedback controllaw is designed to control the bifurcations taking place in the resonance response, thusremoving or delaying the occurrence of jump and hysteresis phenomena. Numericalsimulations are performed to verify the effectiveness of the proposed feedback control.
The stability regions of ship in longitudinal wave are analyzed by the Lyapunov exponents method. A feedback control law is designed to improve the stability of ship inlongitudinal wave, numerical simulations are performed to verify the effectiveness of theproposed feedback control.
The combination of the finite difference method and the successive over relaxationmethod is employed to numerically solve the stationary solutions of FPK equation of ship’snonlinear rolling system． The joint probability density function and stationary meanout-crossing rate are investigated for ship nonlinear rolling subjected to additive white noiseexcitation.
Basing on the nonlinear dynamics theory, the global stability of ship in stochastic beamsea is researched by the global bifurcation method. Considered the stochastic excitation termas bounded noise and the influence of nonlinear damping and nonlinear righting moment, therandom single degree of freedom nonlinear rolling equation is established. The randomMelnikov mean-square criterion is used to analysis the global stability of this system. Theship’s prarmetrical rolling equation in stochastic longitudinal waves is established, theprincipal resonance of the paramerically excited system is investigated. The method ofmultiple scales was used to determine the equations of modulation of amplitude and phase.The stability and steady state response were studied. The influence of ship’s damping, themain frequences of the stochastic wave and the bandwidth of the waves for the ship’s saftyregin in longitudinal waves are analyzed.
引文
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