ARTICLE
Stability and bifurcation analysis for an airfoil model with a high-order nonlinear spring
Shuqun Li 1,2
,

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1
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China

2
Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, China

Submission date: 2021-12-13

Final revision date: 2021-12-27

Acceptance date: 2022-01-03

Online publication date: 2022-02-07

Publication date: 2022-04-30

Corresponding author
Shuqun Li

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, China

Journal of Theoretical and Applied Mechanics 2022;60(2):185-197

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ABSTRACT
In this paper, the stability and bifurcation of an airfoil model with a high-order nonlinear spring are investigated both analytically and numerically. Two possible types of bifurcation at the equilibrium point are studied. It is proved that the zero characteristic root can only be a single zero. With the help of the center manifold theory and the normal form theory, the expressions of critical bifurcation curves leading to initial bifurcation and secondary bifurcation are obtained. Numerical simulations confirm the theoretical results.

REFERENCES (22)
1.
Carroll J.V., Mehra R.K., 1982, Bifurcation analysis of nonlinear aircraft dynamics, Journal of Guidance Control and Dynamics, 5, 529-536.

2.
Golubev V.V., Dreyer B.D., Hollenshade T.M., Visbal M., 2009, High-accuracy viscous simulations of gust-airfoil nonlinear aeroelastic interaction, Proceedings of the 39th American Institute of Aeronautics and Astronautics Fluid Dynamics Conference.

3.
Gordon J.T., Meyer E.E., Minogue R.L., 2008, Nonlinear stability analysis of control surface flutter with freeplay effects, Journal of Aircraft, 45, 1904-1916.

4.
Hao Y., Du X., Hu Y., Wu Z., 2021, Stochastic P-bifurcation of a 3-DOF airfoil with structural nonlinearity, Journal of Theoretical and Applied Mechanics, 59, 307-317.

5.
Hao Y., Wu Z., 2020, Stochastic flutter of multi-stable non-linear airfoil in turbulent flow, Journal of Theoretical and Applied Mechanics, 58, 155-168.

6.
Hu H., 2000, Applied Nonlinear Dynamics, Beijing, Aviation Press.

7.
Knudsen C., Slivsgaard E., Rose M., True H., Feldberg R., 1994, Dynamics of a model of a railway wheelset, Nonlinear Dynamics, 6, 215-236.

8.
Lee C.L., 1986, An iterative procedure for nonlinear flutter analysis, AIAA Journal, 24, 833-840.

9.
Malhotra N., Namachchivaya N.S., 1997, Chaotic motion of shallow arch structures under 1:1 internal resonance, Journal of Engineering Mechanics – ASCE, 123, 620-627.

10.
Namachchivaya N.S., Van Roessel H.J., 1986, Unfolding of degenerate Hopf bifurcation for supersonic flow past a pitching wedge, Journal of Guidance Control and Dynamics, 9, 413-418.

11.
Namachchivaya N.S., Van Roessel H.J., 1990, Unfolding of double-zero eigenvalue bifurcations for supersonic flow past a pitching wedge, Journal of Guidance Control and Dynamics, 13, 343-347.

12.
Rajagopal K., Admassu Y., Weldegiorgis R., Duraisamy P., Karthikeyan A., 2019, Chaotic dynamics of an airfoil with aigher-order plunge and pitch stiffnesses in incompressible flow, Complex, 2019, 1-10.

13.
Schy A.A., Hannah M.E., 1977, Prediction of jump phenomena in roll-coupled maneuvers of airplanes, Journal of Aircraft, 14, 375-382.

14.
Shen S.F., 1959, An aproximate analysis of nonlinear flutter problems, Journal of the Aerospace Sciences, 26, 25-32.

15.
Tharayil M., Alleyne A.G., 2004, Modeling and control for smart Mesoflap aeroelastic control, IEEE/ASME Transactions on Mechatronics, 9, 30-39.

16.
Thompson J.M., 1983, Complex dynamics of compliant off-shore structures, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 387, 407-427.

17.
Woolston D.S., Runyan H.L., Andrews R.E., 1957, An investigation of effects of certain types of structural nonlinearities on wing and control surface flutter, Journal of the Aeronautical Sciences, 24, 57-63.

18.
Wu C., Zhang H., Fang T., 2007, Flutter analysis of an airfoil with bounded random parameters in incompressible flow via Gegenbauer polynomial approximation, Aerospace Science and Technology, 11, 518-526.

19.
Yu P., 1998, Computation of normal forms via a perturbation technique, Journal of Sound and Vibration, 211, 19-38.

20.
Yu P., Huseyin K., 1988, A perturbation analysis of interactive static and dynamic bifurcations, IEEE Transactions on Automatic Control, 33, 28-41.

21.
Zhao L., Yang Z., 1990, Chaotic motions of an airfoil with non-linear stiffness in incompressible flow, Journal of Sound and Vibration, 138, 245-254.

22.
Zhou L., Chen Y., Chen F., 2013, Chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow, Aerospace Science and Technology, 25, 138-144.

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