碰撞振动系统Lyapunov指数谱的计算

摘要

利用Poincaré映射方法将含同隙碰撞振动系统在碰撞截面转化为离散动力系统,构建了系统的映射方程及其Jacobi矩阵,得出碰撞振动系统Lyapunov指数谱的计算方法;通过数值仿真给出了系统的Lyapunov指数谱随参数大范围变化的规律,与相应的分岔图进行对照,验证了其方法的正确性和有效性.%The vibro-impact system with a gap is transformed to the discrete counterpart at the impact section by applying Poincare mapping. The transcendental map and the corresponding Jacobian matrix are constructed, and the calculation of Lyapunov exponential spectrum on the vibro-impact system is obtained. The global parameters-varying rules of the Lyapunov exponential spectrum on this system are analyzed by numerical simulations. Comparing the Lyapunov exponential spectrum diagram with the bifurcation diagram, the validity and feasibility of this method are verified.