Volume 37 Issue 1
Jan.  2011
Turn off MathJax
Article Contents
Fu Li, Wang Qi. Method for estimating largest Lyapunov exponent in non-smooth multibody systems[J]. Journal of Beijing University of Aeronautics and Astronautics, 2011, 37(1): 45-48. (in Chinese)
Citation: Fu Li, Wang Qi. Method for estimating largest Lyapunov exponent in non-smooth multibody systems[J]. Journal of Beijing University of Aeronautics and Astronautics, 2011, 37(1): 45-48. (in Chinese)

Method for estimating largest Lyapunov exponent in non-smooth multibody systems

  • Received Date: 26 Nov 2009
  • Publish Date: 31 Jan 2011
  • According to the theories of both non-smooth mechanics and non-linear dynamics, a numerical method for estimating the largest Lyapunov exponent in non-smooth multi-body systems with unilateral constraints was presented. Lagrange equation of the first kind was applied to derive the structure-varying dynamic equations of the systems and the scheme for linear complementarity problem(LCP) was used to detect non-smooth events, such as stick-slip transition, detachment,collision andsoon.Chaos synchronization method was applied to estimate the largest Lyapunov exponent. The algorithm of bisection and the algorithm of coupling parameter modulation were used to increase the speed of calculation.The numerical results obtained from two examples indicate that the method is effective.

     

  • loading
  • [1] De Souza S L T,Caldas I L.Calculation of Lyapunov exponents in systems with impacts[J].Chaos,Solitons and Fractals,2004,19(3):569-579 [2] Jin L,Lu Q S,Twizell E H.A method for calculating the spectrum of Lyapunov exponents by local maps in non-smooth impact-vibrating systems[J].Journal of Sound and Vibration,2006,298(4/5):1019-1033 [3] Andrzej Stefanski,Tomasz Kapitaniak.Using chaos synchronization to estimate the largest Lyapunov exponent of non-smooth systems [J].Discrete Dynamics in Natural & Society,2000,4:207-215 [4] 王琪,黄克累,陆启韶.树形多体系统非线性动力学的数值分析方法[J].固体力学学报,1999,20(4):363-367 Wang Qi,Huang Kelei,Lu Qishao.A numerical algorithm for nonlinear dynamical analysis of multibody systems with topological tree configuration[J].Acta Mechanica Solida Sinica,1999,20(4):363-367 (in Chinese) [5] 金俐,王琪,陆启韶.树形多体Hamilton 系统的Lyapunov 指数计算方法[J].北京航空航天大学学报,2001,27(2):230-232 Jin Li,Wang Qi,Lu Qishao.A method for calculating the Lyapunov exponents in tree binding multibody Hamiltonian systems[J].Journal of Beijing University of Aeronautics and Astronautics,2001,27(2):230-232(in Chinese) [6] Fu Shihui,Wang Qi.Estimating the largest Lyapunov exponent in a multibody system with dry friction by using chaos synchromization[J].Acta Mechanica Sinica,2006,22(3):277-283 [7] Stefariski A,Kapitaniak T.Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization[J].Chaos,Solitons and Fractals,2003,15(2):233-244 [8] Pfeiffer F.On non-smooth dynamics[J].Meccanica,2008,4(5):533-554 [9] Fu Li,Wang Qi,Wang Shimin.Time-stepping for multibody dynamics with friction-affected bilateral constraints[J].Progress in Natrual Science,2009,19(12),1799-1804 [10] Leine R I,Van Campen D H,Van De Vrande B L.Bifurcations in nonlinear discontinuous systems[J].Nonlinear Dynamics,2000,23(2):105-164
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views(3365) PDF downloads(879) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return