四自由度非线性系统的随机分岔混沌特性研究被引量：1

Random Bifurcation and Chaos Analysis of Nonlinear System with Four DOF

导出

摘要以四自由度迟滞非线性随机振动模型为研究对象,以速度和位移立方的模型来模拟振动系统的迟滞非线性力,并以Monte Carlo法模拟随机位移激励,对迟滞非线性随机系统的动力学特性进行分析.通过系统的Poincare截面、分岔图及最大Lyapunov指数分析了系统迟滞非线性力各参数对系统混沌状态的影响.研究表明,非线性刚度系数对振动系统混沌状态的影响较小,线性阻尼项和线性刚度项次之,而非线性阻尼项的影响最为明显.不仅证明了非线性振动系统随机混沌振动现象的存在,更重要的是可以为非线性振动系统参数的合理取值提供理论依据. A vibration model with nonlinear with four DOF was proposed. A usual cubic velocity and a usual cubic displacement were used to simulate nonlinear hysteretic force of vibration system, and random excitations were simulated with Monte-Carlo method. Based on Poincare section, fork picture and Lyapunov Index, the effect of hysteretic force＇ s parameters of system to chaos was analyzed. The results showed that nonlinear stiffness term affected the least to chaos of vibration system, nonlinear affected secondly, nonlinear damping term affected the most. The article not only proved the existence of random chaos in vibration system with nonlinearity, but also provided theoretical foundation for selecting parameters of vibration system with nonlinearity probably.

作者王云祥方明霞

机构地区同济大学航空航天与力学学院

出处《力学季刊》 CSCD 北大核心 2014年第2期300-307,共8页 Chinese Quarterly of Mechanics

基金国家自然科学基金重点项目(11032009) 国家自然科学基金(51075303)

关键词迟滞非线性随机分岔随机混沌 hysteretic nonlinear system random bifurcation random chaos

分类号 V211.3 [航空宇航科学与技术—航空宇航推进理论与工程]

引文网络
相关文献

参考文献8

1朱位秋.非线性随机动力学与控制研究近期进展[J].强度与环境,2005,32(4):1-5. 被引量：2
2KAPITANIAK T. Chaos in systems with noise[M]. Singapore: World Scientific, 1988.
3LITAK G, BOROWIEC M, FRISWELL M I, et al. Chaotic vibration of a quarter-car model excited by the road surface profile[R]. Technical University of Lublin, 2006.
4LITAK G, BOROWlEC M, FRISWELL M I, et al. Chaotic response of a quarter car model forced by a road profile with a stochastic component[J]. Chaos Solitons Fractals, 2009, 39(2):2448-2456.
5LIU W Y, ZHU W Q, HUANG Z L. Effect of bounded noise on chaotic motion of doffing oscillator under parametric excitation[J]. Chaos Solitons Fractals, 2001, 12:527-537.
6陈立群,刘延柱.一类复杂力场中磁性刚体航天器的混沌姿态运动[J].空间科学学报,2001,21(1):81-85. 被引量：7
7LI J R, XU W, YANG X L, et al. Chaotic motion of van der Pol-Mathieu-Duffing system under bounded noise parametric excitation[J]. J Sound Vib, 2008, 309:330-337.
8ZHANG Y, XU W, FANG T. Stochastic hopf bifuecation and chaos of stochastic bonhoeffer-van del pol system via chebyshev polynomial approximation[J]. Appl Math Comput, 2007, 190:1225-1236.

二级参考文献15

1刘延柱.航天器姿态动力学[M].北京:国防工业出版社,1995.182-211.
2刘延柱，非线性动力学，2000年，217页
3刘延柱，自然科学进展，1998年，8卷，4期，386页
4刘延柱，航天器姿态动力学，1995年，71页
5Stratonovich R L. Topics in the theory of random noise[M]. New York: Gorden and Breach, vol 1, 1963; vol 2, 1967.
6Crandall S H, Mark W D. Random vibration in mechanical system[M]. New York: Academic Press, 1963.
7Lin Y K, Cai G Q. Probabilistic structural dynamics, advanced theory and applications[M]. New York: McGraw-Hill, 1995.
8Gammatitoni L, et al. Stochastic resonance[J]. Reviews of Modern Physics, 1998, 70 (1): 223-287.
9Khasminskii R Z. Stochastic stability of differential equations[M]. Alphen aan den Rijn: Sijthoff & Noordhoff, 1980.
10Fleming W H, Soner H M. Controlled markov processes and viscosity solution[M]. New York: Springer-Verlag, 1992.