一、前言高速自转的转轴,若转轴截面不中心对称,则一般其两个截面主惯矩不等,在某些转速范围内,转轴将回转失稳。对只具有二个自由度的单转子系统,其失稳区为[1,2] ω_1≤Ω≤ω_2 (1—1)其中ω_1、ω_2、对应于二个主惯矩的临界转速,Ω为自转角速度。对多自由度集聚转子系统,或对连续转子系统,也有了许多工作。如[3,4]讨论了离散系统,[5—7]讨论了连续系统。所做工作大多是寻找失稳区位置,大小与数目,以及各种参数对 I. INTRODUCTION High-speed rotation of the shaft, if the shaft cross-section is not symmetrical, the general two of its main section of the moment of inertia, in some speed range, the shaft will rotate instability. For a single-rotor system with two degrees of freedom, the instability zone is [1,2] ω_1≤Ω≤ω_2 (1-1) where ω_1, ω_2 correspond to the critical rotational speeds of the two main moments, and Ω is Rotation angular velocity. There is also a lot of work to be done for a multi-degree-of-freedom rotor system or for a continuous rotor system. Discrete systems are discussed in [3,4], and continuous systems are discussed in [5-7]. Most of the work is to find the location of destabilization, size and number, as well as a variety of parameters