Supercritical and subcritical Hopf bifurcation and limit cycle oscillations of an airfoil with cubic nonlinearity in supersonic\hypersonic flow

Nonlinear Dynamics

Volumn 67, Issue 4, 2012, Pages 2637-2649

  Guo, Hulun ^a   Chen, Yushu ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Floquet theory; Harmonic balance method; LCO; Singularity theory; Supercritical and subcritical Hopf bifurcation

Indexed keywords

FLOQUET THEORY; HARMONIC BALANCE METHOD; LCO; SINGULARITY THEORY; SUPER-CRITICAL;

AIRFOILS; DIFFERENTIAL EQUATIONS; HYPERSONIC FLOW;

HOPF BIFURCATION;

EID: 84858860061     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-011-0177-1     Document Type: Article

References (29)

1. L. Librescu G. Chiocchia P. Marzocca 2003 Implications of cubic physical/aerodynamic nonlinearities on the character of the flutter instability boundary Int. J. Non-Linear Mech. 38 2 173 199 05138133 10.1016/S0020-7462(01) 00054-3
2. Librescu, L., Na, S., Marzocca, P., Chung, C.: Active aeroelastic control of 2-D wing-flap systems in an incompressible flow field. AIAA Paper 2003-1414 (2003)
3. L.K. Abbas C. Qian P. Marzocca G. Zafer A. Mostafa 2008 Active aerothermoelastic control of hypersonic double-wedge lifting surface Chin. J. Aeronaut. 21 8 18 10.1016/S1000-9361(08)60002-3
4. E. Hopf 1942 Bifurcation of a periodic solution from a stationary solution of a system of differential equations Berl. Math. Phys. Klasse, Sachsischen. Akad. Wiss. Leip. 94 3 32
5. B.H.K. Lee S.J. Price Y.S. Wong 1999 Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos Prog. Aerosp. Sci. 35 205 334 10.1016/S0376-0421(98)00015-3
6. P.J. Holmes 1977 Bifurcations to divergence and flutter in flow-induced oscillations: a finite-dimensional analysis J. Sound Vib. 53 4 471 503 0363.73059 10.1016/0022-460X(77)90521-1
7. F. Mastroddi L. Morino 1996 Limit-cycle taming by nonlinear control with application to flutter Aeronaut. J. 100 999 389 396
8. E. Dowell E. John S. Thomas 2003 Nonlinear aeroelasticity J. Aircr. 40 5 857 874 10.2514/2.6876
9. Woolston, D.S., Runyan, H.L., Byrdsong, T.A.: Some effects of system nonlinearities in the problem of aircraft flutter. NACA TN 3539 (1995)
10. D.S. Woolston H.L. Runyan R.E. Andrews 1957 An investigation of effects of certain types of structural nonlinearities on wing and control surface flutter J. Aeronaut. Sci. 24 57 63
11. J.K. Liu L.C. Zhao 1992 Bifurcation analysis of airfoils in incompressible flow J. Sound Vib. 154 1 117 124 0922.76215 10.1016/0022-460X(92) 90407-O
12. B.H.K. Lee L.Y. Jiang Y.S. Wong 1999 Flutter of an airfoil with a cubic restoring force J. Fluids Struct. 13 75 101 10.1006/jfls.1998.0190
13. B.H.K. Lee L. Liu K.W. Chung 2005 Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces J. Sound Vib. 281 699 717 10.1016/j.jsv.2004.01.034
14. L. Liu E.H. Dowell 2004 The secondary bifurcation of an aeroelastic airfoil motion: effect of high harmonics Nonlinear Dyn. 37 1 31 49 2091455 1078.74016 10.1023/B:NODY.0000040033.85421.4d
15. Chen, Y.S., Leung, A.Y.T.: Bifurcation and Chaos in Engineering. Springer, London (1998)
16. L. Liu Y.S. Wong B.H.K. Lee 2000 Application of the centre manifold theory in non-linear aeroelasticity J. Sound Vib. 234 4 641 659 1777014 10.1006/jsvi.1999.2895
17. B.D. Coller P.A. Chamara 2004 Structural non-linearities and the nature of the classic flutter instability J. Sound Vib. 277 711 739 2094262 10.1016/j.jsv.2003.09.017
18. Q. Ding D.L. Wang 2006 The flutter of an airfoil with cubic structural and aerodynamic non-linearities Aerosp. Sci. Technol. 10 427 434 2275148 1195.74080 10.1016/j.ast.2006.03.005
19. P. Yu Z. Chen L. Librescu P. Marzocca 2007 Implications of time-delayed feedback control on limit cycle oscillation of a two-dimensional supersonic lifting surface J. Sound Vib. 304 974 986 2307115 10.1016/j.jsv.2007.03.030
20. P. Shahrzad M. Mahzoon 2002 Limit cycle flutter of airfoils in steady and unsteady flows J. Sound Vib. 256 2 213 225 10.1006/jsvi.2001.4113
21. H. Ashley G. Zartarian 1956 Piston theory-a new aerodynamic tool for the aeroelastician J. Aeronaut. Sci. 23 12 1109 1118 82316
22. L.K. Abbas Q. Chen K. O'Donnell D. Valentine P. Marzocca 2007 Numerical studies of a non-linear aeroelastic system with plunging and pitching freeplays in supersonic/hypersonic regimes Aerosp. Sci. Technol. 11 405 418 10.1016/j.ast.2007.02.007
23. Thuruthimattam, B.J., Friedmann, P.P., McNamara, J.J., Powell, K.G.: Modeling approaches to hypersonic aeroelasticity. ASME International Mechanical Engineering Congress and Exposition, 2002-32943 (2001)
24. P.P. Friedmann J.J. McNamara B.J. Thuruthimattam I. Nydick 2004 Aeroelastic analysis of hypersonic vehicles J. Fluids Struct. 19 681 712 10.1016/j.jfluidstructs.2004.04.003
25. P. Friedmann C.E. Hammond T.H. Woo 1977 Efficient numerical treatment of periodic systems with application to stability problems Int. J. Numer. Methods Eng. 11 1117 1136 472183 0367.73059 10.1002/nme.1620110708
26. Z.M. Ge H.H. Chen 1997 Bifurcations and chaotic motions in a rate gyro with a sinusoidal velocity about the spin axis J. Sound Vib. 200 2 121 137 1433718 10.1006/jsvi.1996.0695
27. Golubitsky, M., Schaeffer, D.G.: Singularities and Groups in Bifurcation Theory, vol. 1. Springer, New York (1985)
28. Golubitsky, M., Schaeffer, D.G.: Singularities and Groups in Bifurcation Theory, vol. 2. Springer, New York (1988)
29. Y.S. Chen W.F. Langford 1988 The subharmonic bifurcation solution of nonlinear Mathieu's equation and Euler dynamically buckling problem Acta Mech. Sin. 20 522 532 1014070