摘要
基于一类规则横浪作用下的单自由度船舶横摇运动模型,考虑恢复力矩和阻尼力矩的非线性因素,以一低干舷船模为例,利用龙格库塔法求解了横摇运动方程,通过时间庞加莱截面绘制了系统的分岔图;考虑其受随机风荷载扰动下不同周期吸引子演变成奇异非混沌吸引子的具体过程,发现周期激励系统在随机激励扰动下同样存在奇异非混沌吸引子,且当分岔参数离混沌区域越远,所需要随机激励的幅值越大才能诱发奇异非混沌吸引子.通过最大李雅普诺夫指数验证吸引子的非混沌性;采用奇异连续谱和分形图刻画吸引子的奇异性.
Based on a single-degree-of-freedom ship sailing in regular beam seas,the nonlinear rolling equation is established.The Runge-Kutta methods is used to solve the differential equation of motion,and the bifurcation diagram is plot by Poincarésurface of section.The process of different periodic attractors transforming into strange nonchaotic attractors under random wind excitation is studied by numerical simulation.It is found that a larger random excitation intensity is required to induce SNAs when the parameter is varied further from the chaotic range.The maximum Lyapunov exponent is used to verify the nonchaotic characteristics of the attractors,and singular continuous spectrum and the trajectories in the complex plane can demonstrate the strange property of the attractors.
作者
何智超
乐源
李高磊
刘润
He Zhichao;Yue Yuan;Li Gaolei;Liu Run(School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 611756,China)
出处
《动力学与控制学报》
2024年第1期52-59,共8页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(12072291,11732014,12172306)。
关键词
船舶横摇
随机激励
奇异非混沌
李雅普诺夫指数
奇异连续谱
ships rolling
stochastic excitation
strange nonchaotic
Lyapunov exponent
singular continuous spectrum
