This paper presents a stochastic model for performing the uncertainty and sensitivity analysis of a Jeffcott rotor system with fixed-point rub-impact and multiple uncertain parameters. A probabilistic nonlinear formulation is developed based on the combination of the harmonic balance method and an alternate frequency/time procedure (HB-AFT) in stochastic form. The non-intrusive generalized polynomial chaos expansion (gPCE) with unknown deterministic coefficients is employed to represent the propagation of uncertainties on rotor dynamics. In conjunction with the path continuation scheme and the Floquet theory, the developed model enables one to expediently evaluate the uncertainty bounds and probability density functions (PDFs) on periodic solution branches and associated stabilities. A global sensitivity analysis is then carried out by evaluating Sobol’s indices from gPCE to quantitatively ascertain the relative influence of different stochastic parameters on vibrational behaviors and conditions for the occurrence of rub-impact. The efficiency of the proposed algorithm for nonlinear stochastic dynamics of rub-impact rotors is validated with Monte Carlo simulation. Parametric studies are finally carried out to investigate the effects of multiple random parameters on the probabilistic variability in nonlinear responses of rub-impact rotors, which reveals the necessary to consider input uncertainties in analyses and designs to ensure the sustainable system performance.

本文提出了一种用于执行定点摩擦冲击和多个不确定参数的Jeffcott转子系统不确定性和灵敏度分析的随机模型。基于谐波平衡法和随机频率/时间程序（HB-AFT）的组合，开发了一种概率非线性公式。确定性系数未知的非侵入式广义多项式混沌展开（gPCE）用于表示转子动力学不确定性的传播。结合路径延续方案和Floquet理论，开发的模型使人们可以方便地评估周期解分支和相关稳定性上的不确定性范围和概率密度函数（PDF）。然后，通过评估来自gPCE的Sobol指数进行全局敏感性分析，以定量确定不同随机参数对振动行为和发生摩擦影响的条件的相对影响。蒙特卡罗仿真验证了所提出的碰摩转子非线性随机动力学算法的效率。最后进行了参数研究，以研究多个随机参数对碰摩转子非线性响应中概率变异性的影响，这揭示了在分析和设计中考虑输入不确定性以确保系统可持续性能的必要性。