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Nonlinear and dual-parameter chaotic vibrations of lumped parameter model in blisk under combined aerodynamic force and varying rotating speed

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Abstract

In this paper, the nonlinear and dual-parameter chaotic vibrations are investigated for the blisk structure with the lumped parameter model under combined the aerodynamic force and varying rotating speed. The varying rotating speed and aerodynamic force are, respectively, simplified to the parametric and external excitations. The nonlinear governing equations of motion for the rotating blisk are established by using Hamilton’s principle. The free vibration and mode localization phenomena are studied for the tuning and mistuning blisks. Due to the mistuning, the periodic characteristics of the blisk structure are destroyed and uniform distribution of the energy is broken. It is found that there is a positive correlation between the mistuning variable and mode localization factor to exhibit the large vibration of the blisk in a certain region. The method of multiple scales is applied to derive four-dimensional averaged equations of the blisk under 1:1 internal and principal parametric resonances. The amplitude–frequency response curves of the blisk are studied, which illustrate the influence of different parameters on the bandwidth and vibration amplitudes of the blisk. Lyapunov exponent, bifurcation diagrams, phase portraits, waveforms and Poincare maps are depicted. The dual-parameter Lyapunov exponents and bifurcation diagrams of the blisk reveal the paths leading to the chaos. The influences of different parameters on the bifurcation and chaotic vibrations are analyzed. The numerical results demonstrate that the parametric and external excitations, rotating speed and damping determine the occurrence of the chaotic vibrations and paths leading to the chaotic vibrations in the blisk.

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All data generated or analyzed during this study are included in this published article.

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Acknowledgements

The authors gratefully acknowledge the support of National Natural Science Foundation of China (NNSFC) through Grant Nos. 11832002, 12072201 and 11427801, the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB) and the funding received from the University of Toronto Advanced Research Laboratory for Multifunctional Lightweight Structures (ARL-MLS).

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Authors and Affiliations

  1. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    W. Zhang & L. Ma

  2. School of Aerospace Engineering, Shenyang Aerospace University, Liaoning, 110136, People’s Republic of China

    Y. F. Zhang

  3. Department of Mechanical & Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canada

    K. Behdinan

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  1. W. Zhang
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Zhang, W., Ma, L., Zhang, Y.F. et al. Nonlinear and dual-parameter chaotic vibrations of lumped parameter model in blisk under combined aerodynamic force and varying rotating speed. Nonlinear Dyn 108, 1217–1246 (2022). https://doi.org/10.1007/s11071-022-07287-9

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