摘要
通过建立弹性地基一般支承输流管道的随机非线性动力学模型,得到Ito随机微分方程,并求解该系统响应扩散过程的转移概率密度函数相应的FPK方程.然后用拟不可积Hamilton理论对系统进行Hopf分岔分析,利用Lyapunov指数和奇异边界理论对该系统的稳定性进行讨论.最后通过模拟平稳概率密度函数和联合概率密度函数的图像对得到的数值结果进行验证.
Firstly,the stochastic nonlinear dynamic model of the system is established and the Ito differentiation equation is obtained.Then,the corresponding FPK equation of the response-transition probability density function with the diffusing process can be got.Secondly,the Hopf bifurcation behavior of the system is studied by using the quasi-nonintegrable Hamilton system theory.Besides,the conditions of local and global stability of the system are discussed by largest Lyapunov exponent and boundary category.Finally,the functional image of stationary probability density and jointly stationary probability density are simulated,and the numerical results are verified.
作者
白宝丽
展之婵
白媛
贾彬霞
BAI Bao-li ZHAN Zhi-chan BAI Yuan JIA Bin-xia(School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Chin)
出处
《兰州文理学院学报（自然科学版）》
2017年第5期23-27,共5页
Journal of Lanzhou University of Arts and Science(Natural Sciences)
基金
国家自然科学基金项目(61364001)
关键词
弹性地基
输流管道
随机稳定性
随机Hopf分岔
elastic foundation
flow conveying pipe
stochastic stability
stochastic Hopf bifurcation
