[en] In recent years there have been several applications of numerical continuation approaches to aeroelastic systems with freeplay. While some of these have been successful, the general application of the method to such systems remains problematic. Numerical continuation can fail in the presence of complex bifurcations, numerous nearby periodic solution branches and other factors. In this paper, a three-part procedure for applying numerical continuation to aeroelastic systems with freeplay is proposed, designed to ensure that the complete periodic behavior is identified, even for systems with very complex bifurcation diagrams. First, the equivalent linearization approach is used to determine approximations to the periodic solutions of the nonlinear system. Then, a shooting-based technique is applied separately to each linearized approximation in order to pinpoint the nearest exact periodic solution. This process results in a cloud of periodic solutions, representing points on all the solution branches and sub-branches. Finally, a branch-following shooting procedure is applied to this cloud of points in order to obtain a complete description of every branch of periodic solutions. The methodology is applied to a simple aeroelastic system with three degrees of freedom and freeplay in the control surface. This system has been often studied but never fully characterised. It is shown that the proposed method succeeds in describing the complete bifurcation behaviour of the system and explaining its limit cycle response.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Dimitriadis, Grigorios ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Interactions Fluide-Structure - Aérodynamique expérimentale
Language :
English
Title :
Shooting-Based Complete Bifurcation Prediction for Aeroelastic Systems with Freeplay
Publication date :
2011
Journal title :
Journal of Aircraft
ISSN :
0021-8669
eISSN :
1533-3868
Publisher :
American Institute of Aeronautics and Astronautics
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Bibliography
Woolston, D. S., Runyan, H. L., and Byrdsong, T. A., "Some Effects of System Nonlinearities in the Problem of Aircraft Flutter," NACATN- 3539, 1955.
Woolston, D. S., Runyan, H. L., and Andrews, R. E., "An Investigation of Effects of Certain Types of Structural Nonlinearities on Wing and Control Surface Flutter," Journal of the Aeronautical Sciences, Vol. 24, No. 1, Jan. 1957, pp. 57-63.
McIntosh, S. C., Jr., Reed, R. E., and Rodden,W. P., "Experimental and Theoretical Study of Nonlinear Flutter," Journal of Aircraft, Vol. 18, No. 12, 1981, pp. 1057-1063. doi:10.2514/3.57600
Yang, Z. C., and Zhao, L. C., "Analysis of Limit Cycle Flutter of an Airfoil in Incompressible Flow," Journal of Sound and Vibration, Vol. 123, No. 1, 1988, pp. 1-13. doi:10.1016/S0022-460X(88)80073-7
Conner, M. D., Tang, D. M., Dowell, E. H., and Virgin, L., "Nonlinear Behaviour of a Typical Airfoil Section with Control Surface Freeplay: a Numerical and Experimental Study," Journal of Fluids and Structures, Vol. 11, No. 1, 1997, pp. 89-109. doi:10.1006/jfls.1996.0068
Marsden, C. C., and Price, S. J., "Transient and Limit Cycle Simulation of a Nonlinear Aeroelastic System," Journal of Aircraft, Vol. 44, No. 1, 2007, pp. 60-70. doi:10.2514/1.21367
Brase, L. O., and Eversman, W., "Application of Transient Aerodynamics to the Structural Nonlinear Flutter Problem," Journal of Aircraft, Vol. 25, No. 11, 1988, pp. 1060-1068. doi:10.2514/3.45703
Hauenstein, A. J., Zara, J. A., Eversman, W., and Qumei, K., "Chaotic and Nonlinear Dynamic Response of Aerosurfaces with Structural Nonlinearities," Proceedings of the 33rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper 92-2547-CP, Dallas, TX, May 1992.
Price, S. J., Lee, B. H. K., and Alighanbari, H., "Postinstability Behaviour of a Two-Dimensional Airfoil with a Structural Nonlinearity," Journal of Aircraft, Vol. 31, No. 6, 1994, pp. 1395-1401. doi:10.2514/3.46664
Theodorsen, T., "General Theory of Aerodynamic Instability and the Mechanism of Flutter," NACATR-496, 1935.
Tang, D.,Dowell, E. H., andVirgin, L. N., "Limit Cycle Behaviour of an Airfoil with a Control Surface," Journal of Fluids and Structures, Vol. 12, No. 7, 1998, pp. 839-858. doi:10.1006/jfls.1998.0174
Kholodar, D. B., and Dowell, E. H., "Behavior of Airfoil with Control Surface Freeplay for Nonzero Angles of Attack," AIAA Journal, Vol. 37, No. 5, 1999, pp. 651-653. doi:10.2514/2.766
Virgin, L. N., Dowell, E. H., and Conner, M. D., "On the Evolution of Deterministic Non-Periodic Behavior of an Airfoil," International Journal of Non-Linear Mechanics, Vol. 34, No. 3, 1999, pp. 499-514. doi:10.1016/S0020-7462(98)00038-9
Friedmann, P. P., "Renaissance of Aeroelasticity and Its Future," Journal of Aircraft, Vol. 36, No. 1, 1999, pp. 105-121. doi:10.2514/2.2418
Lee, B. H. K., Price, S. J., and Wong, Y. S., "Nonlinear Aeroelastic Analysis of Airfoils: Bifurcation and Chaos," Progress in Aerospace Sciences, Vol. 35, No. 3, 1999, pp. 205-334. doi:10.1016/S0376-0421(98)00015-3
Liu, L., and Dowell, E. H., "Harmonic Balance Approach for an Airfoil with a Freeplay Control Surface," AIAA Journal, Vol. 43, No. 4, 2005, pp. 802-815. doi:10.2514/1.10973
Alighanbari, H., and Price, S. J., "The Post-Hopf-Bifurcation Response of an Airfoil in Incompressible Two-Dimensional Flow," Nonlinear Dynamics, Vol. 10, No. 4, 1996, pp. 381-400. doi:10.1007/BF00045483
Doedel, E., Paffenroth, R. C., Champneys, A., Fairgrieve, T., Kuznetsov, Y., Oldeman, B. E., Sandstede, B., and Wang, X., AUTO 2000: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont), User's Guide, 2000.
Allgower, E. L., and Georg, K., Numerical Continuation Methods: An Introduction, Springer-Verlag, New York, 1990.
Jones, D. P., Roberts, I., and Gaitonde, A. L., "Identification of Limit Cycles for Piecewise Nonlinear Aeroelastic Systems," Journal of Fluids and Structures, Vol. 23, No. 7, 2007, pp. 1012-1028. doi:10.1016/j. jfluidstructs.2007.03.007
Roberts, I., Jones, D. P., Lieven, N. A. J., Bernado, M. D., and Champneys, A. R., "Analysis of Piecewise Linear Aeroelastic Systems Using Numerical Continuation," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 216, No. 1, 2002, pp. 1-11. doi:10.1243/0954410021533382
Dimitriadis, G., "Continuation of Higher Order Harmonic Balance Solutions for Nonlinear Aeroelastic Systems," Journal of Aircraft, Vol. 45, No. 2, 2008, pp. 523-537. doi:10.2514/1.30472
Gordon, J. T., Meyer, E. E., and Minogue, R. L., "Nonlinear Stability Analysis of Control Surface Flutter with Freeplay Effects," Journal of Aircraft, Vol. 45, No. 6, 2008, pp. 1904-1916. doi:10.2514/1.31901
Dimitriadis, G., "Numerical Continuation of Aeroelastic Systems: Shooting vs Finite Difference Approach," RTO-MP-AVT-152 Limit Cycle Oscillations and Other Amplitude-Limited Self-Excited Vibrations, NATO Research & Technology OrganizationNo. AVT- 152-025, Loen, Norway, May 2008.
Strogatz, S. H., Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Perseus Books, Cambridge, MA, 1994.
Peeters, M., Viguié, R., Kerschen, G., and Golinval, J.-C., "Nonlinear Normal Modes, Part II: Toward a Practical Computation Using Numerical Continuation Techniques," Mechanical Systems and Signal Processing, Vol. 23, No. 1, 2009, pp. 195-216. doi:10.1016/j.ymssp.2008.04.003
Dimitriadis, G., "Bifurcation Analysis of Aircraft with Structural Nonlinearity and Freeplay Using Numerical Continuation," Journal of Aircraft, Vol. 45, No. 3, 2008, pp. 893-905. doi:10.2514/1.28759
Gerald, C. F., and Wheatley, P. O., Applied Numerical Analysis, 5th ed., Addison-Wesley, Reading, MA, 1990.
Seydel, R., Practical Bifurcation and Stability Analysis, 3rd ed., Springer, New York, 1994.
Leine, R. I., and Neijmeijer, H., Practical Bifurcation and Stability Analysis, Springer Verlag, New York, 2004.
Kuznetsov, Y. A., Elements of Applied Bifurcation Theory, 2nd ed., Springer, New York, 1998.
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