船舶横摇混沌阈值的数值方法研究  

Research on numerical method of ship-roll chaos threshold

作　　者：刘亚冲 LIU Ya-chong(Research Division,Marine Design&Research Institute of China,Shanghai 200011,China)

机构地区：[1]中国船舶及海洋工程设计研究院基础研究部,上海200011

出　　处：《船舶力学》2019年第2期135-141,共7页Journal of Ship Mechanics

摘　　要：为计算梅尔尼科夫函数的简单零点,文章比较分析了两种数值算法:类帕德逼近和高斯—勒让德积分,作为验证,计算了某激励频率下系统的李雅普诺夫指数谱。然后选取某型船,采用梅尔尼科夫函数方法计算了横摇动力系统的混沌阈值,观察了横摇系统的安全池随外激励增大而逐渐破损的过程,并追踪了破损域中某点的相轨迹。研究计算表明:类帕德逼近可以较精确地得到同(异)宿轨道的参数方程,但在方程的设解形式上需要一定的技巧性,且计算量较大;高斯—勒让德积分不关注参数方程具体形式,处理简单,便于工程计算。In order to calculate the simple zero point of Melnikov function,two numerical methods namely Quasi-Pade approximation and Gauss-Legendre integration are compared and analyzed.As identification,the Lyapunov exponents spectra are calculated under given frequency of exciting force.Then a specific type of ship is selected and Melnikov method is used to calculate the chaos threshold of ship-roll dynamical system.The erosion process of the safe basin along with the increasing exciting force is observed,besides,the phase trajectory of breakage points is traced.Research shows that Quasi-Pade approximation is prone to get the accurate parametric equation of homoclinic(heteroclinic)orbit,but it requires certain skills in formation of preinstall solution of equation,and it needs much calculation.Gauss-Legendre integration neglects the specific forms of parametric equation,and it is simple to handle and convenient for engineering application.

关 键 词：梅尔尼科夫函数 类帕德逼近 高斯—勒让德积分 混沌阈值 李雅普诺夫指数 安全池 

分 类 号：U661.1[交通运输工程—船舶及航道工程]