Abstract
We follow two approaches to derive the normal form that represents the aeroelastic response of the Goland wing. Such a form constitutes an effective tool to model the main physical behaviors of aeroelastic systems and, as such, can be used for developing a phenomenological reduced-order model. In the first approach, an approximation of the wing’s response near the Hopf bifurcation is constructed by directly applying the method of multiple scales to the two coupled partial-differential equations of motion. In the second approach, we apply the same method to a Galerkin discretized model that is based on the mode shapes of a cantilever beam. The perturbation results from both approaches are verified by comparison with results from numerical integration of the discretized equations.
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References
Dowell, E.H., Tang, D.: Nonlinear aeroelasticity and unsteady aerodynamics. AIAA J. 40, 1697–1707 (2002)
Gilliatt, H.C., Strganac, T.W., Kurdila, A.J.: An investigation of internal resonance in aeroelastic systems. Nonlinear Dyn. 31, 1–22 (2003)
Beran, P.S., Strganac, T.W., Kim, K., Nichkawde, C.: Studies of store-induced limit-cycle oscillations using a model with full system nonlinearities. Nonlinear Dyn. 37, 329–339 (2004)
Abbas, L.K., Chen, Q., Marzocca, P., Milanese, A.: Non-linear aeroelastic investigations of store(s)-induced limit cycle oscillations. J. Aerospace Eng. 222, 63–80 (2008)
Nayfeh, A.H.: Method of Normal Forms. Wiley Series in Nonlinear Science. Wiley, New York (1993)
Ghommem, M., Hajj, M.R., Nayfeh, A.H.: Uncertainty analysis near hopf bifurcation of an aeroelastic system. J. Sound Vib. 329, 3335–3347 (2010)
Ghommem, M., Nayfeh, A.H., Hajj, M.R.: Control of limit cycle oscillations of a two-dimensional aeroelastic system. Math. Probl. Eng. 2010, 782457 (2010)
Dimitriadis, G., Vio, G.A., Cooper, J.E.: Stability and limit cycle oscillations amplitude prediction for simple nonlinear aeroelastic systems. In: Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA (2004). AIAA Paper No. 2004-1693
Leng, G.: Reduced-order nonlinear analysis of aircraft dynamics. J. Guid. Control Dyn. 18, 361–364 (1995)
Kim, K., Strganac, T.W.: Nonlinear response of a cantilever wing with an external store. In: Proceedings of the 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Norfolk, VA (2003). AIAA Paper No. 2003-1708
Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley, New York (1983)
Nayfeh, A.H.: Perturbation Methods. Wiley, New York (1973)
Nayfeh, A.H., Hammad, B.K., Hajj, M.R.: Discretization effects on flutter aspects of wing/store configurations. J. Vib. Control (in press)
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Nayfeh, A.H., Ghommem, M. & Hajj, M.R. Normal form representation of the aeroelastic response of the Goland wing. Nonlinear Dyn 67, 1847–1861 (2012). https://doi.org/10.1007/s11071-011-0111-6
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DOI: https://doi.org/10.1007/s11071-011-0111-6