碰撞振动系统的最大Lyapunov指数计算

Calculation of maximum Lyapunov exponent for vibro-impact system

借助彗尾映射和Khasminskii变换,构造了碰撞振动系统存在碰撞、颤碰以及黏滞3种情形下的最大Lyapunov指数计算格式。以单边约束形状记忆合金梁模型为例,分析系统在碰撞、颤碰以及黏滞下的Lyapunov指数序列,并讨论系统的分岔和混沌运动,结合时间历程图和相图验证了所构造的最大Lyapunov指数算法的有效性。

With the help of discontinuous mapping and tail mapping,the maximum Lyapunov exponent of the system with the above three structures was constructed using Khasminskii transform.For the shape memory alloy beam model with unilateral constraints,the corresponding Lyapunov exponent sequences were analyzed and the bifurcation and chaotic motions of the system were discussed.The results show that the validity of the maximum Lyapunov exponent algorithm is verified by combining the time history diagram and phase diagram.