非线性系统周期强迫不平衡响应的稳定性分析

多自由度强非线性系统是工程实际中经常遇见的一类模型，利用非线性动力学分析中的打靶法求解该类系统的周期解，并对Flopuet主导特征值判断周期解的失稳方式，利用该方法对旋转机械中的一个具体模型；双盘县臂柔性转子-非同心型挤压油膜阻尼器（SFD）系统周期强迫不平衡响应的稳定性和分岔行为进行了分析，分析表明，在该系统中存在着第二Hopf分岔、倍周期分岔、鞍-结分岔三种分岔形式。

THE ANALYSIS ON THE STABILITY OF RESPONSES OF STRONG NONLINEAR SYSTEM SUBJECTED TO PERIODIC UNBALANCE FORCE

In modern engine, the rotor-bearing system that is typical nonlinear dynamic system has been wide used. While modern rotating machinery has been designed with weigher load, higher rotating speed, and lighter weight, the stability of system become critical problem. As a kind of typical nonlinear system with multi-freedom degrees, the rotor-bearing system can become unstable by various elements such as fluid film force of bearing, etc. Those elements, to be strictly, are all nonlinear force and can be linearized under certain condition. With the development of nonlinear dynamics, especially bifurcation and chaos theories are applied to analyze nonlinear rotor-bearing system, the dynamic characteristics of complicate rotor-nonlinear supporting system can be studied with numerical stimulation method. Until now, the analysis on strong nonlinear dynamic system is limited to system with a few freedom degrees. Owing to the strong nonlineaxity of squeeze film force, the theoretical analysis on it is very difficult. In this paper, a multi-freedom dynamic system with high nonlinearity-flexible rotor with two disks supported on squeeze film damper system is investigated. In order to get the periodic solution, the time domain method -Shooting Method is adopted, then avoid solving a series of large order nonlinear equations of frequency method.While the unbalance response of this system is obtained, the Floquet theory has the advantage to judge how the leading Floquet multiplier cross the unit circle and how the system become unstable. It is found that there are three kinds of way for periodic solution becoming unstable in this system: second Hopf bifurcation, doubling bifurcation and saddle-node bifurcation. The result by theoretical analysis is compared with that by direct integration and they are identical, so the theoretical analysis is right. The divergence of shoot method is also analyzed.