非线性系统周期强迫不平衡响应的稳定性分析

摘要

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Floquet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: 双盘悬臂柔性转子-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.%In modern engine, the rotor-bearing system that is typical nonlineardynamic system has been wide used. While modern rotating machinery hasbeen designed with weigher load, higher rotating speed, and lighterweight, the stability of system become critical problem.rn　　As a kind of typical nonlinear system with multi-freedom degrees,the rotor-bearing system can become unstable by various elementssuch as fluid film force of bearing, etc. Those elements, to bestrictly, are all nonlinear force and can be linearized undercertain condition. With the development of nonlinear dynamics,especially bifurcation and chaos theories are applied to analyzenonlinear rotor-bearing system, the dynamic characteristics ofcomplicate rotor-nonlinear supporting system can be studied withnumerical stimulation method. Until now, the analysis on strongnonlinear dynamic system is limited to system with a few freedomdegrees.rn　　Owing to the strong nonlinearity of squeeze film force, thetheoretical analysis on it is very difficult. In this paper, amulti-freedom dynamic system with high nonlinearity -flexiblerotor with two disks supported on squeeze film damper system isinvestigated. In order to get the periodic solution, the timedomain method -Shooting Method is adopted, then avoid solvinga series of large order nonlinear equations of frequency method.While the unbalance response of this system is obtained, theFloquet theory has the advantage to judge how the leadingFloquet multiplier cross the unit circle and how the systembecome unstable. It is found that there are three kinds of wayfor periodic solution becoming unstable in this system: secondHopf bifurcation, doubling bifurcation and saddle-nodebifurcation.rn　　The result by theoretical analysis is compared with that bydirect integration and they are identical, so the theoreticalanalysis is right.rn　　The divergence of shoot method is also analyzed.