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Stability and bifurcation for limit cycle oscillations of an airfoil with external store

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Abstract

In this paper, stability and local bifurcation behaviors for the nonlinear aeroelastic model of an airfoil with external store are investigated using both analytical and numerical methods. Three kinds of degenerated equilibrium points of bifurcation response equations are considered. They are characterized as (1) one pair of purely imaginary eigenvalues and two pairs of conjugate complex roots with negative real parts; (2) two pairs of purely imaginary eigenvalues in nonresonant case and one pair of conjugate complex roots with negative real parts; (3) three pairs of purely imaginary eigenvalues in nonresonant case. With the aid of Maple software and normal form theory, the stability regions of the initial equilibrium point and the explicit expressions of the critical bifurcation curves are obtained, which can lead to static bifurcation and Hopf bifurcation. Under certain conditions, 2-D tori motion may occur. The complex dynamical motions are considered in this paper. Finally, the numerical solutions achieved by the fourth-order Runge–Kutta method agree with the analytic results.

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Acknowledgements

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NNSFC) through Grant nos. 11572148 and 11172125, and the National Research Foundation for the Doctoral Program of Higher Education of China through Grant no. 20133218110025. Meanwhile, the authors thank for the suggestions of the reviewers, which are beneficial to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Li Zhang

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Fangqi Chen

  3. School of Mathematics and Physics, Anhui University of Technology, Ma’anshan, 243002, People’s Republic of China

    Li Zhang

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  1. Li Zhang
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Correspondence to Li Zhang.

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Zhang, L., Chen, F. Stability and bifurcation for limit cycle oscillations of an airfoil with external store. Nonlinear Dyn 88, 165–187 (2017). https://doi.org/10.1007/s11071-016-3237-8

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  • DOI: https://doi.org/10.1007/s11071-016-3237-8

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