平面多体机械系统的随机稳定性及Hopf分岔分析

白宝丽; 张建刚; 杜文举; 卢家荣

doi:10.3969/j.issn.1003-0972.2017.03.003

平面多体机械系统的随机稳定性及Hopf分岔分析

1. 兰州交通大学数理学院, 甘肃兰州 730070;
2. 兰州交通大学交通运输学院, 甘肃兰州 730070

基金项目:

国家自然科学基金项目(61364001)

详细信息

作者简介:
白宝丽(1989-),女,山西吕梁人,硕士生;张建刚(1978-),男,甘肃庆阳人,副教授,博士,主要从事非线性动力系统研究.

中图分类号: TP271
计量
- 文章访问数: 744
- HTML全文浏览量: 43
- PDF下载量: 3
出版历程
- 收稿日期: 2016-10-19
- 修回日期: 2017-02-28
- 发布日期: 2017-07-09

Stochastic Stability and Hopf Bifurcation Behavior of Planar Multi-Body Mechanical System

1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China;
2. School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

摘要

摘要: 首先建立平面多体机械系统的随机非线性动力学模型,得到Itô随机微分方程,求解了系统响应扩散过程的转移概率密度函数相应的FPK方程.然后运用拟不可积Hamilton理论对平面多体机械系统进行Hopf分岔分析,利用Lyapunov指数和奇异边界理论对该系统的局部和全局稳定性分别进行讨论.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验证了理论结果.
- 平面多体机械系统 /
- 拟不可积Hamilton理论 /
- 随机平均法 /
- 随机稳定性 /
- 随机Hopf分岔
Abstract: Firstly,the stochastic nonlinear dynamic model of the multi-body mechanical system was established, the Itô differentiation equation and the corresponding FPK equation of the response-transition probability density function with the diffusing process were obtained.Then,the Hopf bifurcation behavior of the planar multi-body mechanical system was studied by using the quasi-nonintegrable Hamilton system theory.The conditions of local and global stability of the system were discussed by largest Lyapunov exponent and boundary category.Finally,the functional image of stationary probability density and jointly stationary probability density were simulated to verify the theorectical results.
- multi-body mechanical system /
- quasi-nonintegrable Hamilton system theory /
- stochastic stability /
- stochastic Hopf bifurcation

HTML全文

参考文献(13)

[1]	ZHAO Bo, ZHOU Kun, XIE Youbai. A new numerical method for planar multi-body system with mixed lubricated revolute joint[J]. International Journal of Mechanical Sciences, 2016, 113(7):105-119.
[2]	LAI Xiongming, HE Huang, LAI Qinfang, et al. Computational prediction and experimental validation of revolute joint clearance wear in the low-velocity planar mechanism[J]. Mechanical Systems and Signal Processing, 2017, 85(2):963-976.
[3]	BAI Zhengfeng, SUN Yi. A study on dynamics of planar multi-body mechanical systems with multiple revolute clearance joints[J]. European Journal of Mechanics, 2016, 60(11):95-111.
[4]	LUO Shaokai, HE Jinman, XU Yanli, et al. Fractional generalized Hamilton method for equilibrium stability of dynamical systems[J]. Applied Mathematics Letters, 2016, 60(10):14-20.
[5]	滕俊超,朱位秋.谐和与宽带随机激励下拟可积哈密顿系统的最优时滞控制[J].振动工程学报,2016,29(2):207-213. TENG Junchao, ZHU Weiqiu. Optimal time-delay control of quasi integrable Hamiltonian systems under combined harmonic and wide-band random excitations[J]. Journal of Vibration Engineering, 2016, 29(2):207-213.
[6]	白宝丽,张建刚,闫宏明.一类随机的SIR流行病模型的动力学行为分析[J].山东大学学报(理学版),2017,52(4):14-24. BAI Baoli, ZHANG Jiangang, YAN Hongming. The dynamic behavior analysis of a stochastic SIR epidemic model[J]. Journal of Shandong University (Natural Science), 2017, 52(4):14-24.
[7]	GU Xudong, ZHU Weiqiu. A stochastic averaging method for analyzing vibro-impact systems under Gaussian white noise excitations[J]. Journal of Sound and Vibration, 2014, 333(9):2632-2642.
[8]	朱位秋.非线性随机动力学与控制-Hamilton理论体系框架[M].北京:北京科学出版社,2003:130-395. ZHU Weiqiu. Nonlinear stochastic dynamics and control-Hamilton theory system framework[M]. Beijing:Beijing Science Press, 2003:130 -395.
[9]	ZHU Weiqiu, HUANG Zhilong. Stochastic averaging of quasi-Integrable hamiltonian systems[J]. Journal of Sound & Vibration, 1997, 64(4):178-195.
[10]	JIA Wantao, ZHU Weiqiu. Stochastic averaging of quasi-integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitations[J]. Nonlinear Dynamics, 2014, 76(2):1271-1289.
[11]	KHASMINSKⅡ R. Stochastic stability of differential equations[C]//Stochastic Modelling & Applied Probability. Springer, 2012:221-231.
[12]	CHIGANSKY P. An ergodic theorem for filtering with applications to stability[J]. Systems & Control Letters, 2006, 55(11):908-917.
[13]	ZHU W Q, HUANG Z L. Stochastic Hopf bifurcation of quasi-nonintegrable-Hamiltonian systems[J]. International Journal of Non-Linear Mechanics, 1999, 34(3):437-447.