发电机组转子轴系扭振模化系统的三重共振

建立了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．研究了系统的固有频率存在双重内共振关系ω３≈２ω２，ω２≈２ω１且Ω≈ω２时的三重共振问题．文中应用非线性振动的改进平均法，求得了系统三重共振的一次近似解，对三重共振的定常解进行了理论分析和数值计算，并进行了奇异性分析，文中指出三重共振解具有双饱和特性，对二种主要的理论分析和数值计算结果进行了实验验证，实验结果与理论结果相符．

TRIPLE RESONANCES OF TORSIONAL VIBRATION OF A SHAFTING SYSTEM SIMULATING A GENERATOR SET ROTOR

A mathematical model of torsional vibration of the shafting system which has quadratic nonlinearities and harmonic excitation is established. By using of the improved averaging method for nonlinear oscillation, under the conditions ω 3≈2ω 2, ω 2≈2ω 1,and  Ω ≈ω 2, the first approximation solution and its corresponding steady-state solution of the triple resonances are obtained. The steady-state response curves are obtained and the singularity analysis is carried out. It is pointed out that the tr...