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Evaluation of the Centre Manifold Method for Limit Cycle Calculations of a Nonlinear Structural Wing | ||
| AUT Journal of Modeling and Simulation | ||
| مقاله 12، دوره 41، شماره 2، بهمن 2009، صفحه 33-41 اصل مقاله (338.42 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/miscj.2009.238 | ||
| نویسندگان | ||
| Morteza Dardeli؛ Firooz Bakhtiari-Nejadii | ||
| چکیده | ||
| In this study the centre manifold is applied for reduction and limit cycle calculation of a highly nonlinear structural aeroelastic wing. The limit cycle is arisen from structural nonlinearity due to the large deflection of the wing. Results obtained by different orders of centre manifolds are compared with those obtained by time marching method (fourth-order Runge-Kutta method). These comparisons show zero, third and fifth order manifolds are very good approximation of this system. The aeroelastic model is a low aspect ratio rectangular cantilevered wing in a low subsonic flow which is structurally modeled by the Von Karman plate theory. A continuous time reduced order modified vortex lattice aerodynamics model is utilized in aerodynamics modeling. | ||
| کلیدواژهها | ||
| Centre manifold؛ Limit Cycle؛ Nonlinear aeroelasticity؛ Von Karman plate؛ Domain of attraction | ||
| عنوان مقاله [English] | ||
| Evaluation of the Centre Manifold Method for Limit Cycle Calculations of a Nonlinear Structural Wing | ||
| چکیده [English] | ||
| In this study the centre manifold is applied for reduction and limit cycle calculation of a highly nonlinear structural aeroelastic wing. The limit cycle is arisen from structural nonlinearity due to the large deflection of the wing. Results obtained by different orders of centre manifolds are compared with those obtained by time marching method (fourth-order Runge-Kutta method). These comparisons show zero, third and fifth order manifolds are very good approximation of this system. The aeroelastic model is a low aspect ratio rectangular cantilevered wing in a low subsonic flow which is structurally modeled by the Von Karman plate theory. A continuous time reduced order modified vortex lattice aerodynamics model is utilized in aerodynamics modeling. | ||
| کلیدواژهها [English] | ||
| Centre manifold, Limit Cycle, Nonlinear aeroelasticity, Von Karman plate, Domain of attraction | ||
| مراجع | ||
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[1] E. H. Dowell, J. Edwards, and T. W. Strganac, Nonlinear Aeroelasticity, J. Aircraft, 40 (5) (2003) 857-874. [2] Liu, L., Wong, Y. S., and Lee, B.H.K, Journal of Sound and Vibration 2002, 234(4), 641-659, Application of the centre manifold theory in non-linear aeroelasticity. [3] Shahrzad, P. and Mahzoon, M., Journal of Sound and Vibration 2002 256(2), 213-225, Limit cycle flutter of airfoils in steady and unsteady flows. [4] Dess, D., Mastroddi, F., and Morino, L., Journal of Sound and Vibration 2002 256 (2) 347-365, Limit cycle stability reversal near a Hopf bifurcation with aeroelastic applications. [5] Dess, D., Mastroddi, F., Journal of Fluids and Structures 2004 19, 765-783, Limit cycle stability reversal via singular perturbation and wing flap flutter. [6] Grzedzinski, J., Journal of Fluids and Structures 2005, 21, 187-209, Limitation of application of the centre manifold reduction in aeroelasticity [7] Qian , D., and Li, W. D., Aerospace Science and Technology 2006, 10, 427-434, The flutter of an airfoil with cubic structural and aerodynamic nonlinearities. [8] Bi, Q.S., Yu, P., Journal of Computer and Applied Mathematics 1999, 102, 195-220, Symbolic computation of normal forms for semi-simple cases. [9] K.C. Hall, AIAA Journal, 1994, 32 (12) 2426-2423 Eigenanalysis of Unsteady Flows About Airfoils, Cascades, and Wings. [10] D. Tang, E.H. Dowell and K.C. Hall, AIAA Journal, 1999, 37 (3) 364-371 Limit Cycle Oscillation of a Cantilevered Wing in Low Subsonic Flow. [11] M. Behbahani-Nejad, H. Haddadpour, and V. Esfahanian, Journal of Aircraft 2005, 42 (4) 882-886, Reduced-Order modeling of unsteady flows without static correction requirement Books: [12] Dowell, E.H., Aeroelasticity of Plates ans Shells, Kluwer/Noordhoff International Publishing, Leyden, 1975. [13] Meirovitch, L., Principles and Techniques of Vibrations, Prentice-Hall International INC. 1997. [14] J. Katz and A. Plotkin 1991, Low Speed Aerodynamics, From Wing Theory to Panel Methods, MCGRAW – HILL ,New York. [15] J. Carr 1981 Application of Centre Manifold Theory, New York, Springer-Verlag. | ||
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