多自由度回转系统的参变振动

On the Parametric Excitation of a Gyroscopic System Having Multidegrees of Freedom

对于一个具有周期性系数回转系统的稳定性问题,本文给出了一个一般的分析方法。利用作者提供的一个定理和多尺度法得出了一阶渐近解。讨论了当参数激励频率ρ接近2ω_(?)或ω_(?)+ω_(?)情况下的稳定性问题,并导出了在这些情况下的不稳定域范围。

In this paper, a common procedure for analyzing the stability of a gyroscopic system with periodic coefficients is presented. The first approximation is obtained by means of a theorem given by the author and the method of multiple scales. The stability for the cases when the parametric excitation frequency is nearly equal to 2 ω_i or ω_i +ω_i are discussed, and the instability regions of these cases are derived.