多自由度参激系统稳定性分析的数值解法

The study on dynamic stability of a parametric excitation system mainly focuses on the main unstable region. In order to obtain more results of the combined unstable region, the solution form of Bolotin method under different period numbers was applied with the Floquet method. Combined with the eigen value analysis method, the direct numerical solution method for determining the dynamic unstable region of the multi-dof parametric system is obtained. According to the stability analysis of a two-degree-of-freedom rotating shafting with periodic axial force, the high order unstable region is obtained with the increase of approximate terms of solution, and the boundary of each unstable region tends to be stable with the increase of approximate terms. It is found that the damping makes the boundary of each unstable region "smooth". The method can be applied for general multi-dof periodic parametric damped system and produces a simple and direct numerical solution.