Pedestal looseness and supporting stiffness nonlinearities usually occur in rotating machines. To enhance the robustness and accurately forecast the nonlinear behaviors of rotor systems, these two kinds of common nonlinearities should be considered so that to meet the requirements of the dynamical design of a multi-disk rotor system. In this paper, the rotor system model with cubic supporting stiffness and looseness fault is established by the Lagrange method. The harmonic balance (HB) and Runge–Kutta (RK) methods are used to solve the dynamic response of the double disk rotor system, and the accuracy of the HB method is justified in comparison to the RK method. The bifurcation diagram, time history, frequency spectrum, phase portrait and Poincaré map are provided to discuss the individual and coupling effects of these two nonlinearities on the transient and steady-state response. The obtained experimental results indicate that the proposed model can capture the main nonlinear behaviors of looseness fault and nonlinear supporting stiffness, verifying the accuracy of theoretical and numerical results.

基座松动和支撑刚度非线性通常发生在旋转机器中。为了提高转子系统的鲁棒性和准确预测转子系统的非线性行为，应考虑这两种常见的非线性，以满足多盘转子系统的动力学设计要求。本文采用拉格朗日方法建立了具有三次支撑刚度和松动故障的转子系统模型。采用谐波平衡(HB)和龙格-库塔(RK)方法求解双盘转子系统的动态响应，与RK方法相比，HB方法的精度是合理的。分岔图、时程、频谱、提供相图和庞加莱图来讨论这两种非线性对瞬态和稳态响应的单独和耦合影响。实验结果表明，该模型能够捕捉松动故障和非线性支撑刚度的主要非线性行为，验证了理论和数值结果的准确性。