三质量发电机组轴系扭振模化系统的双重共振

DOUBLE RESONANCES OF A SHAFTING SYSTEM SIMULATING A THREE CONCENTRATED MASS GENERATOR SET ROTOR

建立了三质量发电机组转子轴系扭振模化系统的数学模型，此模型具有平方非线性并受简谐激励作用，应用非线性振动的改进平均法，求得了系统的固有频率与外激励频率存在双重共振关系ω２≈２ω１且Ω≈ω２时的一次近似解及对应的定常解．对定常解进行了理论分析和数值计算，指出系统响应曲线存在饱和、跳跃现象，在某些参数域上有多解共存现象，对两种参数的响应曲线进行了实验研究，实验结果与理论结果相符．

In this paper,a mathematical model of torsional vibration of the shafting system which has quadratic nonlinearities and harmonic excitation is established.By using the method of averaging for nonlinear oscillation under the conditions ω 2≈2ω 1 and Ω≈ω 2 ,the first approximation solution and its corresponding steady state solution of the double resonance are obtained.The theoretical analysis and numerical analysis are made and steady state response curves are obtained.It is pointed out that the double resonance has abundant dynamic phenomenon including periodic ones;coexistence of multiple stable motions and the attendant jumps;and saturation.Two kinds of main response curves are confirmed experimentally.The results of theoretical analysis are shown to be in good agreement with experimental results.