Abstract: In order to predict the vibration response of the high-speed flexible rotor system in aero-engine more accurately and provide technical support for the vibration suppression of the whole engine，dynamical model with respect to rotor system of practical aero-engine is established on the basis of investigating the characteristics of its main structure and nonlinear characteristics of bending stiffness resulting from joint structure. Then numerical harmonic balance method with FFT and Broyden method was put forward to solve the dynamic model，and the degree of freedom was condensed in frequency domain，which can reduce the size of equation and improve the solving efficiency. The method is applied to a test rotor，and the results show that the method in this paper can be 10 times faster than traditional numerical integration. Vibration response of the low rotor system in aero-engine with nonlinear support was analyzed using this paper’s method，which indicated the applicability of the method in engineering.

Key words: Local nonlinear stiffness；Flexible rotor system；Numerical harmonic balance method；Vibration response

摘要： 为了更加精确地预测航空发动机高速柔性转子系统振动响应，为整机振动抑制提供技术支撑，以实际航空发动机转子系统为对象，对其主体结构特征及其连接结构所引起的弯曲刚度非线性特征进行了论述，在此之上建立了其动力学模型。针对这种具有局部非线性刚度的复杂转子系统动力学模型，结合FFT和Broyden迭代方法发展了一种数值谐波平衡法，通过频域方程中的自由度缩减，降低了方程规模，大幅度提高了求解效率。将该方法应用于试验转子的动力特性求解，结果表明:本文方法相比经典数值积分方法可以节省10倍以上时间。采用此方法对涡扇发动机低压转子系统在局部非线性刚度下的动力响应规律进行了分析，论证了论文方法的工程适用性。

关键词: 局部非线性刚度；柔性转子系统；数值谐波平衡法；振动响应