Nonlinear stochastic dynamics of a rub-impact rotor system with probabilistic uncertainties

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.