一种非线性系统周期解的延拓算法

A continuation algorithm for periodic solutions of nonlinear dynamical system

提出了一种非线性系统周期解的延拓算法。指出了非线性系统周期解在分岔点处由于雅可比矩阵奇异而导致一般延拓方法延拓失败问题;然后基于推广的打靶法的思想,将普通延拓算法推广,提出了一种用于周期解延拓的算法。对于非线性动力系统,该算法可以在已知某一参数下的周期解的基础上,求解出在一定参数范围内非线性动力系统的解随参数的连续变化情况。应用该方法对非线性柔性转子-轴承系统的周期解与参数的依赖关系进行了求解,验证了方法的有效性。

A continuation algorithm for periodic solutions of nonlinear dynamical system is presented in this paper.Firstly,continuation failure problem is pointed out that using general continuation algorithm to determine the relationship of the solution and the parameter of the nonlinear system in bifurcation point because of the singularity of Jacobian matrix.Then,based on the idea of the shooting method,by generalizing the general continuation algorithm,a sort of continuation algorithm is presented for continuing periodic solution of nonlinear system.This algorithm can solve the solution under a certain range of parameters based on the known periodic solution under a particular parameter of the nonlinear system.As an example,the dependence relationship of the periodic solution and the parameter is solved using this algorithm for an eight-dimensional flexible rotor-bearing system.The validity of this algorithm is verified by the numerical results obtained in the example.