【作者】 谷家扬；

【导师】 唐友刚；

【作者基本信息】 天津大学 ， 船舶与海洋结构物设计制造， 2005， 硕士

【摘要】 本文应用Melnikov函数及随机动力学的现代理论和方法,研究船舶在随机横浪中的非线性横摇运动和倾覆问题。主要研究内容和成果为:考虑阻尼与恢复力矩的非线性及波浪的随机性,建立了随机横浪中激励力矩的表达式及随机海浪中船舶非线性横摇运动微分方程。求FPK方程近似解,研究白噪声激励下船舶非线性横摇运动的联合概率密度函数及稳定期望穿阈率,应用Melnikov函数和相空间转移率研究船舶在随机波浪中的强非线性横摇运动及其倾覆问题,考虑波浪特征周期、有义波高及船舶阻尼特性的变化规律,推导了船舶在随机横浪中的极限波高的表达式。以长30.7m、宽6.9m的渔船为例,采用ISSC双参数波浪谱,在时域内计算了Melnikov函数,得到了相空间转移率与Melnikov函数之间的关系以及有义波高对相空间转移率的影响,绘制了不同特征周期下允许的极限波高的临界曲线,此外采用白噪声海浪模型,求出了白噪声激励的临界阈值强度。研究了船舶初始倾斜情况下的Melnikov函数和相空间转移率随外部激励、船舶自身阻尼特性的变化特点,求出了随机海浪中具有初始倾角船舶的极限波高的表达式。研究结果表明:随有义波高增大,相空间转移率不断增大,船舶航行的安全域迅速减小,研究结果揭示了相空间转移率与船舶倾覆的内在联系。考虑不同有义波高和特征波浪周期建立的极限波高曲线,可以用来确定船舶航行安全准则。更多还原

【Abstract】 Nonlinear rolling motion and capsizing of ships in random beam seas areinvestigated combining the Melnikov function and modern theory of stochasticdynamics. The main content and achievements in this thesis are as following:The expression of excitation moment of random beam seas is given in this paper.The differential equation of ships nonlinear rolling motion in random seas isestablished considering the nonlinear damping, nonlinear restoring moment andrandom characteristic of wave moment. The approximate solution to FPK equation isobtained. The joint probability density function and stationary mean out-crossing rateare investigated for ship nonlinear rolling subjected to additive white noise excitation.Melnikov function and phase space flux are applied to analyze highly nonlinear rolland capsizing of ships in the random seas. The variation of phase space flux withrespect to the characteristic wave period, significant wave height and damping ofships is studied. The expression of critical wave height of ships in random beam seasis presented in the paper. Considering a fish vessel of 30.7 long and 6.9m wide, the ISSC wave spectrumis used for determining the coefficients of wave, the Melnikov function iscomputed in the time domain. The relation between the phase space flux andMelnikov function is obtained and the influence of significant wave height onphase space flux is also shown. The curves of critical wave height are plotted overa range of characteristic wave period. The white noise is also adopted as theexcitation and the critical strength of white noise is given is this paper. Thevariation of Melnikov function and the rate of phase space flux with respected tothe external excitation and damping characteristic of biased ship in random beamseas are also analyzed. Numerical simulations show that phase space flux is growing continually alongwith significant wave height and the safe basin of ships is decreasing rapidly. Theclosed relations between the phase space flux and ship capsize are revealed. Thecritical curves that established by different significant wave height andcharacteristic wave period may be provided for the safe standard of ships.更多还原