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Noise-induced transition in a piecewise smooth system by generalized cell mapping method with evolving probabilistic vector

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Abstract

In this paper, noise-induced transition behaviors in a piecewise smooth rotor/stator rubbing system subject to additive noise are investigated, with the knowledge of its deterministic global characteristics. In particular, an effective approach based on the parallel generalized cell mapping method with evolving probabilistic vector, or GCM with EPV in short, is introduced, which can efficiently capture the large probability transition in high-dimensional and non-smooth systems. Since there are several multi-stable regions in the rubbing rotor system, both noise-induced explosive and dangerous bifurcations are observed with the variation of the noise intensity within the regions. The noise may induce several times increase in the magnitude of the rotor deflection. The results may be helpful to understand the effect of noise on the qualitative change in the responses of the piecewise smooth rotor/stator rubbing system.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11332008 and 11672218).

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Authors and Affiliations

  1. State Key Laboratory for Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, 28, Xianning West Road, Xi’an, 710049, Shaanxi, People’s Republic of China

    Zigang Li, Jun Jiang & Ling Hong

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  1. Zigang Li
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  2. Jun Jiang
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  3. Ling Hong
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Correspondence to Jun Jiang.

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Li, Z., Jiang, J. & Hong, L. Noise-induced transition in a piecewise smooth system by generalized cell mapping method with evolving probabilistic vector. Nonlinear Dyn 88, 1473–1485 (2017). https://doi.org/10.1007/s11071-016-3323-y

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  • DOI: https://doi.org/10.1007/s11071-016-3323-y

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