Homotopy analysis method for limit cycle oscillations of an airfoil with cubic nonlinearities

JVC/Journal of Vibration and Control

Volumn 16, Issue 2, 2010, Pages 163-179

  Chen, Y M ^a   Liu, J K ^b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b SUN YAT SEN UNIVERSITY   (China)

Author keywords

Airfoil; Homotopy analysis method; Limit cycle oscillation.; Nonlinear aeroelastic system

Indexed keywords

AEROELASTIC SYSTEM; ALGEBRAIC EQUATIONS; CUBIC NONLINEARITIES; EMBEDDING PARAMETERS; HIGH DEGREE OF ACCURACY; HIGH-ORDER APPROXIMATION; HOMOTOPY ANALYSIS METHODS; INVERSE PROPORTIONS; LIMIT CYCLE OSCILLATIONS; NONLINEAR AEROELASTIC SYSTEM; NONLINEAR PROBLEMS; POWER SERIES; SIMPLE ITERATION; SQUARE ROOTS; TWO-DIMENSIONAL AIRFOILS;

AIRFOILS; CONTROL NONLINEARITIES; FIGHTER AIRCRAFT; LINEARIZATION;

NONLINEAR ANALYSIS;

EID: 76349105754     PISSN: 10775463     EISSN: 17412986     Source Type: Journal    
DOI: 10.1177/1077546308097268     Document Type: Review

References (17)

1. Alexander, J.C. and Yorke, J.A., 1978, " The homotopy continuation method: Numerically implementable topological procedures, " Transactions of the American Mathematical Society 242, 271-284.
2. El-Wakil, S.A. and Abdou, M.A., 2008, " New applications of the homotopy analysis method, " Zeitschrift für Naturforschung A 63, 385-392.
3. Jones, R.T., 1940, The Unsteady Lift of a Wing of Finite Aspect Ratio, NACA Report 681.
4. Lee, B.H.K., Gong, L., and Wong, Y.S., 1997, " Analysis and computation of nonlinear dynamic response of a two-degree-of-freedom system and its application in aeroelasticity, " Journal of Fluids and Structures 11, 225-246.
5. Lee, B.H.K., Liu, L., and Chung, K.W., 2005, " Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces, " Journal of Sound and Vibration 281, 699-717.
6. Lee, B.H.K., Price, S.J., and Wong, Y.S., 1999, " Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos, " Progress in Aerospace Science 35, 205-344.
7. Liao, S.J., 2003, Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton, FL.
8. Liao, S.J., 2004, " An analytic approximate approach for free oscillations of self-excited system, " International Journal of Non-Linear Mechanics 39, 271-280.
9. Liu, J.K. and Zhao, L.C., 1992, " Bifurcation analysis of airfoils in incompressible flow, " Journal of Sound and Vibration 154 (1). 117-124.
10. Liu, L., Wong, Y.S., and Lee, B.H.K., 2000, " Application of the center manifold theory in nonlinear aeroelasticity, " Journal of Sound and Vibration 234, 641-659.
11. Liu, L.P. and Dowell, E.H., 2004, " The secondary bifurcation of an aeroelastic airfoil motion: Effect of high harmonics, " Nonlinear Dynamics 37, 31-49.
12. Liu, L.P., Dowell, E.H., and Thomas, J.P., 2007, " A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces, " Journal of Fluids and Structures 23, 351-363.
13. Nayfeh, A.H., 1981, Introduction to Perturbation Techniques, Wiley, New York.
14. Price, S.J., Alighanbari, H., and Lee, B.H.K., 1995, " The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities, " Journal of Fluids and Structures 9, 175-193.
15. Raghothama, A. and Narayanan, S., 1999, " Nonlinear dynamics of a two-dimensional airfoil by incremental harmonic balance method, " Journal of Sound and Vibration 226 (3). 493-517. (Pubitemid 129533336)
16. Shahrzad, P. and Mahzoon, M., 2002, " Limit cycle flutter of airfoils in steady and unsteady flows, " Journal of Sound Vibration 256 (2). 213-225.
17. Ueda, T. and Dowell, E.H., 1984, " Flutter analysis using nonlinear aerodynamic forces, " Journal of Aircraft 21, 101-109.