船舶横纵摇耦合运动突变特性分析

Catastrophe analysis in coupled pitch-roll ship motion

采用非线性动力学理论和突变理论研究了二自由度船舶摇摆的非线性运动.用多尺度法求解正弦调制激励下船舶横纵摇耦合运动的非线性微分方程,得到系统的稳态解,并分析其稳定性.通过对分叉响应方程的计算,获取稳态解处的分歧点集,进而分析系统的突变特性,确定突变类型.数值分析结果表明,当ω1=1,μ1=0.015,2μ=0.015,α1=2.1时,随着F1的变化分歧点曲面存在尖点型突变,且在一定波浪力矩条件下,船舶运动幅值将产生分支突变,从而引起横摇幅值的突跳,此现象可能导致船舶倾覆.

Nonlinear dynamic theory and catastrophe theory were adopted to study two-degrees-of-freedom nonlinear motion of ships. Using multiple scale perturbation techniques, the nonlinear differential equations of a ship＇s cou- pled pitch -roll motion during modulated amplitude sinusoidal excitation were solved. The stability of this solution was analyzed. Calculation of the bifurcation response equation was used to obtain the bifurcation set near the peri- odic solution. Catastrophe properties were analyzed sequentially to ascertain the catastrophe type. The results of nu- merical analysis show that the cusp of catastrophe exists in a bifurcation set surface when ω1=1,μ1 =0. 015,μ2=0.015,α1=2. 1. Under some conditions, the excitation forces bring a ship＇s rolling amplitude to the point of em- branchment catastrophe. Such catastrophic phenomena may lead to a ship capsizing.