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Control of cross-flow-induced vibrations of square cylinders using linear and nonlinear delayed feedbacks

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Abstract

We investigate the effectiveness of linear and nonlinear time-delay feedback controls to suppress high amplitude oscillations of an elastically mounted square cylinder undergoing galloping oscillations. A representative model that couples the transverse displacement and the aerodynamic force is used. The quasi-steady approximation is used to model the galloping force. A linear analysis is performed to investigate the effect of linear time-delay controls on the onset speed of galloping and natural frequencies. It is demonstrated that a linear time-delay control can be used to delay the onset speed of galloping. The normal form of the Hopf bifurcation is then derived to characterize the type of the instability (supercritical or subcritical) and to determine the effects of the linear and nonlinear time-delay parameters on their outputs near the bifurcation. The results show that the nonlinear time-delay control can be efficiently implemented to significantly reduce the galloping amplitude and suppress any dangerous behavior by converting any subcritical Hopf bifurcation into a supercritical one.

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Acknowledgments

The authors gratefully acknowledge the support provided by the Program for New Century Excellent Talents in University (NCET-11-0183) and the Fundamental Research Funds for the Central Universities, HUST (2013TS034, 2014YQ007).

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Authors and Affiliations

  1. Department of Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China

    H. L. Dai, L. Wang & W. B. Liu

  2. Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan, 430074, China

    H. L. Dai, L. Wang & W. B. Liu

  3. Department of Engineering Science and Mechanics, MC 0219, Virginia Tech, Blacksburg, VA, 24061, USA

    A. Abdelkefi

Authors
  1. H. L. Dai
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  2. A. Abdelkefi
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  3. L. Wang
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  4. W. B. Liu
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Correspondence to L. Wang.

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Dai, H.L., Abdelkefi, A., Wang, L. et al. Control of cross-flow-induced vibrations of square cylinders using linear and nonlinear delayed feedbacks. Nonlinear Dyn 78, 907–919 (2014). https://doi.org/10.1007/s11071-014-1485-z

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  • DOI: https://doi.org/10.1007/s11071-014-1485-z

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