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

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Abstract

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.

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Acknowledgements

The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China (NSFC, Grant No. 51975354).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai, 200240, People’s Republic of China

    Zhenguo Zhang, Xinxing Ma & Hongxing Hua

  2. Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

    Xihui Liang

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  1. Zhenguo Zhang
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  2. Xinxing Ma
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  4. Xihui Liang
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Correspondence to Zhenguo Zhang.

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Zhang, Z., Ma, X., Hua, H. et al. Nonlinear stochastic dynamics of a rub-impact rotor system with probabilistic uncertainties. Nonlinear Dyn 102, 2229–2246 (2020). https://doi.org/10.1007/s11071-020-06064-w

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  • DOI: https://doi.org/10.1007/s11071-020-06064-w

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