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http://dx.doi.org/10.12989/sem.2008.30.1.067

On the limit cycles of aeroelastic systems with quadratic nonlinearities  

Chen, Y.M. (Department of Mechanics, SunYat-sen University)
Liu, J.K. (Department of Mechanics, SunYat-sen University)
Publication Information
Structural Engineering and Mechanics / v.30, no.1, 2008 , pp. 67-76 More about this Journal
Abstract
Limit cycle oscillations of a two-dimensional airfoil with quadratic and cubic pitching nonlinearities are investigated. The equivalent stiffness of the pitching stiffness is obtained by combining the linearization and harmonic balance method. With the equivalent stiffness, the equivalent linearization method for nonlinear flutter analysis is generalized to address aeroelastic system with quadratic nonlinearity. Numerical example shows that good approximation of the limit cycle can be obtained by the generalized method. Furthermore, the proposed method is capable of revealing the unsymmetry of the limit cycle; however the ordinary equivalent linearization method fails to do so.
Keywords
aeroelastic system; quadratic nonlinearity; limit cycle; equivalent linearization method;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
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1 Caughey, T.K. (1963), "Equivalent linearization techniques", J. Acoust. Soc. Am., 35(11), 1706-1711   DOI
2 Coller, B.D. and Chamara, P.A. (2004), "Structural non-linearities and the nature of the classic flutter instability", J. Sound Vib., 277, 711-739   DOI   ScienceOn
3 Ding, Q.S., Chen, A.R. and Xiang, H.F. (2002a), "A state space method for coupled flutter analysis of long-span bridges", Struct. Eng. Mech., 14(4), 491-504   DOI   ScienceOn
4 Hall, K.C., Thomas, J.P. and Dowell, E.H. (2000), "Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows", AIAA J., 38, 1853-1862   DOI   ScienceOn
5 Lee, B.H.K., Price, S.J. and Wong, Y.S. (1999a), "Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos", Progress Aerosp. Sci., 35, 205-344   DOI   ScienceOn
6 Liu, J.K. and Zhao, L.C. (1992), "Bifurcation analysis of airfoils in incompressible flow", J. Sound Vib., 154(1), 117-124   DOI   ScienceOn
7 Liu, L.P., Thomas, J.P., Dowell, E.H., Attar, P.J. and Hall, K.C. (2006), "A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator", J. Comput. Phys., 215(1), 298-320   DOI   ScienceOn
8 Wang, Q. (2003), "On complex flutter and buckling analysis of a beam structure subjected to static follower force", Struct. Eng. Mech., 16(5), 533-556   DOI
9 Ding, Q.S. and Xiang, H.F. (2002b), "Coupled buffeting response analysis of long-span bridges by the CQC approach", Struct. Eng. Mech., 14(5), 505-520   DOI   ScienceOn
10 Chowdhury, A.G. and Sarkar, P.P. (2004), "Identification of eighteen flutter derivatives", Wind & Struct., 7, 187-202   DOI   ScienceOn
11 Lee, B.H.K., Jiang, L.Y. and Wong, Y.S. (1999b), "Flutter of an airfoil with cubic restoring force", J. Fluids Struct., 13, 75-101   DOI   ScienceOn
12 Gu, M., Chen, W., Zhu, L.D., Song, J.Z. and Xiang, H.F. (2001), "Flutter and buffeting responses of the Shantou Bay Bridge", Wind & Struct., 4, 505-518   DOI   ScienceOn
13 Lim, C.W. and Wu, B.S. (2003), "A new analytical approach to the Duffing-harmonic oscillator", Phys. Lett. A, 311, 365-373   DOI   ScienceOn
14 Qin, X.R. and Gu, M. (2004), "Determination of flutter derivatives by stochastic subspace identification technique", Wind & Struct., 7, 173-186   DOI   ScienceOn
15 Shahrzad, P. and Mahzoon, M. (2002), "Limit cycle flutter of airfoils in steady and unsteady flows", J. Sound Vib., 256(2), 213-225   DOI   ScienceOn
16 Yang, Y.R. (1995), "KBM method of analyzing limit cycle flutter of a wing with an external store and comparison with wind tunnel test", J. Sound Vib., 187(2), 271-280   DOI   ScienceOn
17 Moon, S.K. and Lee, D.G. (2002), "Efficient models for analysis. of a multistory structure with flexible wings", Struct. Eng. Mech., 13(5), 465-478   DOI   ScienceOn
18 Tang, D., Dowell, E.H. and Virgin, L.N. (1998), "Limit cycle behaviour of an airfoil with a control surface", J. Fluids Struct., 12, 839-858   DOI   ScienceOn
19 Thomas, J.P., Dowell, E.H. and Hall, K.C. (2004), "Modeling viscous transonic limit cycle oscillation behavior using a harmonic balance approach", J. Aircraft, 41(6), 1266-1274   DOI   ScienceOn
20 Zhao, L.C. and Yang, Z.C. (1989), "Chaotic motions of an airfoil with nonlinear stiffness in incompressible flow", J. Sound Vib., 138(2), 245-254
21 Chamara, P.A. and Coller, B.D. (2004), "A study of double flutter", J. Fluids Struct., 19, 863-879   DOI   ScienceOn