有界噪声激励下船舶横摇系统的响应分析  

Response Analysis of Nonlinear Ship Rolling Motion Under Bounded Noises

作　　者：郑丽文[1] 王神龙 Zheng Liwen;Wang Shenlong(School of Mechatronic Engineering,Quzhou College of Technology,Quzhou 324000,China;School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]衢州职业技术学院机电工程学院,衢州324000 [2]上海理工大学机械工程学院,上海200093

出　　处：《动力学与控制学报》2023年第5期35-43,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金面上项目(12172226);浙江省访问工程师项目(FG2021218)。

摘　　要：本文提出了一种改进的基于Jacobi椭圆函数的随机平均法,用于求解有界噪声激励下船舶横摇系统的随机响应问题.对谐波及有界噪声激励下的船舶横摇模型进行了局部灵敏度分析,研究了系统参数对船舶横摇角的影响,为之后随机分析奠定了基础.通过引入Jacobi椭圆函数,导出随机微分方程,应用随机平均法得到了关于横摇运动幅值和相位的伊藤方程,进一步求解相应的Fokker-Planck-Kolmogorov(FPK)方程,得到幅值概率密度.将该方法应用于有界噪声激励下船舶横摇系统,研究了系统的随机响应特性,通过与蒙特卡洛数值模拟结果比较验证了该方法的可行性与准确性.该方法所得的随机响应结果与灵敏度分析结果一致:激励幅值E,外激频率Ω,线性刚度系数γ对船舶横摇系统产生较大的影响,其余参数不影响船舶横摇运动的振幅,只对概率峰值的高度有影响.In this paper,a stochastic averaging method based on elliptic function is proposed to evaluate the probabilistic solution of ship roll motion excited by bounded noises.We carry out local sensitivity analysis on the rolling model to analyze the influence of main parameters,thus laying a foundation for the random analysis.By introducing the Jacobi elliptic functions(JEFs),we acquire the stochastic differential equation and the It equation regarding the amplitude and phase of the roll motion.Then,we obtain the probabilistic solutions of the rolling system by solving the corresponding Fokker-Planck-Kolmogorov(FPK)equation.Then apply this method to investigate the probabilistic solution of ship’s nonlinear rolling motion under bounded noise excitation,which shows perfect agreement with the sensitivity quantification.Finally,the feasibility and accuracy of the proposed technique are verified by the Monte Carlo simulations.

关 键 词：JACOBI椭圆函数 随机平均法 船舶横摇 随机响应 灵敏度分析 

分 类 号：O324[理学—一般力学与力学基础] O322[理学—力学]