Plural Shooting Method for Solving Plural ODE and Its Applications to Nonlinear Rotordynamics

摘要

The plural shooting method is proposed for the aim of calculating periodic solutions of plural ODE and analyzing their stabilities in a high dimension dynamical system. The relationships of Jacobians and monodromy matrices between the plural ODE and the corresponding real ODE were proved respectively. According to these relationships, the Floquet multipliers of real ODE can be calculated, and then the stabilities of periodic solutions of plural ODE obtained by plural shooting can be analyzed. The method was applied to a nonlinear 2-spans rotor system with 16-DOF, giving the bifurcation diagrams of the solutions varying with the external excitation frequency. Compared with the direct integral method, the plural shooting method has high efficiency and good stability for large-scale nonlinear rotor systems.