规则波中船舶艏摇运动失稳及横甩临界波高分析

Analysis of the Yaw Motion Instability and Critical Wave Height of Ship Broaching Motion in Regular Wave

本文研究了船舶艏摇运动失稳及发生横甩运动的临界波高.建立船舶艏摇运动响应单自由度方程模拟船舶艏摇运动,以内倾船为例,分别采用多尺度法和龙格库塔法求解艏摇运动方程.基于多尺度法求出了运动方程的1阶近似解,给出了艏摇运动是否发生失稳的条件以及稳定运动的参数域.针对解析方法得到的稳定域和非稳定域范围,分别选取稳定域和不稳定域内的典型工况,数值求解船舶横艏摇运动方程,得到船舶艏摇角的运动时历曲线,通过数值方法对解析结果进行验证.分析遭遇频率为船舶固有频率的2倍及不同波高下的运动响应特性,通过艏摇角的时间历程曲线和相图判断船舶是否发生横甩失稳现象,得出了船舶的艏摇运动幅值随波高的变化趋势.船舶在2倍频下的艏摇运动随波高变化出现分岔,由分岔图确定船舶发生横甩的临界波高.研究表明,本文建立的艏摇运动和横甩分析模型,采用非线性动力学的分岔方法分析船舶的艏摇运动失稳和预报横甩的临界条件,可以用于进行波浪中船舶的横甩分析,是一种可行的方法.船舶艏摇运动方程中的参数激励项随波高的增加逐渐增加,达到临界波高后,船舶的艏摇角响应幅值会大幅度地增加,船舶发生横甩失稳运动.

This research focuses on the instability of a ship’s yaw motion and the critical wave height of the broaching.A single-degree-of-freedom equation of the yaw motion was established.Taking a tumblehome ship as an example,an analytical method(multi-scale method)and a numerical simulation method(Runge-Kutta method)were applied to solve the yaw motion equation.With the multi-scale method,a first-order approximate solution of the equation was obtained.Moreover,the conditions for the instability of the yaw motion and the range of the stability region were obtained.Considering the range of stable and unstable regions obtained by the analytical method,the typical conditions in the stable and unstable regions were selected.A numerical method was used to solve the equation of the yaw motion,and the time history series of the yaw angle was obtained.The analytical results were verified by comparing them with those of the numerical methods.The nonlinear dynamic characteristics of the ship under different conditions wherein the encounter frequency is twice the natural frequency were calculated by numerical simulations.The time history and phase diagram of the yaw motion were calculated to determine if the ship underwent broaching and was unstable,and the tendency of the ship yaw motion amplitude with wave height was also obtained.Finally,a bifurcation diagram of the ship’s yaw motion was drawn to determine the critical wave height of broaching.The yaw motion and broaching motion model are established in this paper using the nonlinear dynamic bifurcationmethod to analyze the instability of the ship’s yaw motion and predict the critical wave height of the broaching motion.This analytical method can be used to analyze the ship’s broaching motion in regular waves,and the feasibility of themethod is proved. The parameter excitation term in the ship’s yaw motion equation gradually increases with an increasein the wave height. After reaching the critical wave height,the amplitude of the ship’s yaw angle response willgreatly increase,and the ship will undergo a broaching motion.