GUO Hu-lun, CHEN Yu-shu. Dynamic Analysis of a Two-Degree-of-Freedom Airfoil With Freeplay and Cubic Nonlinearities in Supersonic Flow[J]. Applied Mathematics and Mechanics, 2012, 33(1): 1-13. doi: 10.3879/j.issn.1000-0887.2012.01.001
Citation: GUO Hu-lun, CHEN Yu-shu. Dynamic Analysis of a Two-Degree-of-Freedom Airfoil With Freeplay and Cubic Nonlinearities in Supersonic Flow[J]. Applied Mathematics and Mechanics, 2012, 33(1): 1-13. doi: 10.3879/j.issn.1000-0887.2012.01.001

Dynamic Analysis of a Two-Degree-of-Freedom Airfoil With Freeplay and Cubic Nonlinearities in Supersonic Flow

doi: 10.3879/j.issn.1000-0887.2012.01.001
  • Received Date: 2011-06-02
  • Rev Recd Date: 2011-09-18
  • Publish Date: 2012-01-15
  • The nonlinear aeroelastic response of a two-dimensional airfoil with freeplay and cubic nonlinearities in supersonic flow were investigated. The second-order piston theory was employed to analyze a double wedge airfoil. Then, the fold bifurcation and the amplitude jump phenomenon were detected using averaging method and multi-variable Floquet theory. The analytical results were further verified by numerical simulations. Lastly, the influence of the freeplay parameters on the aeroelastic response was analyzed in detail.
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  • [1]
    Abbas L K, Qian C, Marzocca P, Zafer G, Mostafa A. Active aerothermoelastic control of hypersonic double-wedge lifting surface[J]. Chinese Journal of Aeronautics, 2008, 21(1): 8-18.
    [2]
    Librescu L, Chiocchia G, Marzocca P. Implications of cubic physical/aerodynamic nonlinearities on the character of the flutter instability boundary[J]. International Journal of Non-Linear Mechanics, 2003, 38(2): 173-199.
    [3]
    Hyun D H, Lee I. Transonic and low-supersonic aeroelastic analysis of a two-degree-of-freedom airfoil with a freeplay non-linearity[J]. Journal of Sound and Vibration, 2000, 234(5): 859-880.
    [4]
    Liu L, Song Y S. Non-linear aeroelastic analysis using the point transformation method, part 1—freeplay model[J]. Journal of Sound and Vibration, 2002, 253(2): 447-469.
    [5]
    Roberts I, Jones D P, Lieven N A J, Bernado M D, Champneys A R. Analysis of piecewise linear aeroelastic systems using numerical continuation[J]. Journal of Aeronautical Engineering, 2002, 216(1): 1-11.
    [6]
    陈衍茂, 刘济科. 非线性颤振系统中既是超临界又是亚临界的Hopf分岔点研究[J]. 应用数学和力学, 2008, 29(2): 181-187.(CHEN Yan-mao, LIU Ji-ke. Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems[J]. Applied Mathematics and Mechanics(English Edition), 2008, 29(2): 181-187.)
    [7]
    Liu L, Wong Y S, Lee B H K. Application of the center manifold theory in nonlinear aeroelasticity[J]. Journal of Sound and Vibration, 2000, 234(4): 641-659.
    [8]
    Chung K W, Chan C L, Lee B H K. Bifurcation analysis of a two-degree-of-freedom aeroelastic system with freeplay structural nonlinearity by a perturbation-incremental method[J]. Journal of Sound and Vibration, 2007, 299(3): 520-539.
    [9]
    Chen Y M, Liu J K. Homotopy analysis method for limit cycle oscillations of an airfoil with cubic nonlinearities[J]. Journal of Vibration and Control, 2010, 16(2): 163-179.
    [10]
    Raghothama A, Narayanan S. Non-linear dynamics of a two-dimensional airfoil by incremental harmonic balance method[J]. Journal of Sound and Vibration, 1999, 226(3): 493-517.
    [11]
    Gordon J T, Meyer E E, Minogue R L. Nonlinear stability analysis of control surface flutter with free-play effects[J]. Journal of Aircraft, 2008, 45(6): 1904-1916.
    [12]
    Shen S F. An approximate analysis of nonlinear flutter problems[J]. Journal of the Aerospace Sciences, 1959, 25(1): 25-32.
    [13]
    Yang Y R. KBM method of analyzing limit cycle flutter of a wing with an external store and comparison with a wind-tunnel test[J]. Journal of Sound and Vibration, 1995, 187(2): 271-280.
    [14]
    Kim S H, Lee I. Aeroelastic analysis of a flexible airfoil with a freeplay nonlinearity[J]. Journal of Sound and Vibration, 1996, 193(4): 823-846.
    [15]
    Dimitriadis G. Bifurcation analysis of aircraft with structural nonlinearity and freeplay using numerical continuation[J]. Journal of Aircraft, 2008, 45(3): 893-905.
    [16]
    Zhao D M, Zhang Q C. Bifurcation and chaos analysis for aeroelastic airfoil with freeplay structural nonlinearity in pitch[J]. Chinese Physics B, 2010, 19(3): 1-10.
    [17]
    Conner M D, Tang D M, Dowell E H, Virgin L N. Nonlinear behavior of a typical airfoil section with control surface freeplay: a numerical and experimental study[J]. Journal of Fluids and Structures, 1997, 11(1): 89-109.
    [18]
    Tang D, Dowell E H. Flutter and limit-cycle oscillations for a wing-store model with freeplay[J]. Journal of Aircraft, 2006, 43(2): 487-503.
    [19]
    Tang D, Dowell E H, Virgin L N. Limit cycle behavior of an airfoil with a control surface[J]. Journal of Fluids and Structures, 1998, 12(7): 839-858.
    [20]
    Tang D, Conner M D, Dowell E H. Reduced-order aerodynamic model and its application to a nonlinear aeroelastic system[J]. Journal of Aircraft, 1998, 35(2): 332-338.
    [21]
    Liu L, Dowell E H. Harmonic balance approach for an airfoil with a freeplay control surface[J]. AIAA Journal, 2005, 43(4): 802-815.
    [22]
    Lin W B, Cheng W H. Nonlinear flutter of loaded lifting surfaces  and [J]. Journal of the Chinese Society of Mechanical Engineers, 1993, 14(5): 446-466.
    [23]
    Ashley H, Zartarian G. Piston theory—a new aerodynamic tool for the aeroelastician[J]. Journal of the Aeronautical Sciences, 1956, 23(12): 1109-1118.
    [24]
    Abbas L K, Chen Q, O’Donnell K, Valentine D, Marzocca P. Numerical studies of a non-linear aeroelastic system with plunging and pitching freeplays in supersonic/hypersonic regimes[J]. Aerospace Science and Technology, 2007, 11(5): 405-418.
    [25]
    Friedmann P P, McNamara J J, Thuruthimattam B J, Nydick I. Aeroelastic analysis of hypersonic vehicles[J]. Journal of Fluids and Structures, 2004, 19(5): 681-712.
    [26]
    Lee B H K, Price S J, Wong Y S. Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos[J]. Progress in Aerospace Sciences, 1999, 35(3): 205-334.
    [27]
    Nayfeh A H, Mook D T. Nonlinear Oscillations[M].1st ed. New York: Wiley, 1979.
    [28]
    Nayfeh A H. Perturbation Methods[M]. 1st ed. New York: Wiley, 1973.
    [29]
    Friedmann P, Hammond C E, Woo T H. Efficient numerical treatment of periodic systems with application to stability problems[J]. International Journal of Numerical Methods in Engineering, 1977, 11(7): 1117-1136.
    [30]
    Ge Z M, Chen H H. Bifurcations and chaotic motions in a rate gyro with a sinusoidal velocity about the spin axis[J]. Journal of Sound and Vibration, 1997, 200(2): 121-137.
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