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。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ω１＋ω２≈ω３且Ω≈ω３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，指出系统存在周期解，周期２的概周期运动，响应存在饱和、跳跃现象，在某些参数域上有多解共存现象。 The mathematical model of the torsional vibration system of the rotor shaft of a generator set is established. The model has the square nonlinearity and is subject to the harmonic excitation. By using the improved averaging method of nonlinear vibration, a first-order approximate solution and its corresponding steady-state solution with the double resonance relation ω1 + ω2 ≈ ω3 and Ω ≈ ω3 have been obtained. The theoretical analysis and numerical analysis It is pointed out that the system has periodic solution, almost periodic motion in period 2, saturation and jump in response, and coexistence of multiple solutions in some parameter domains.