Document Type : Original Article

Authors

1 Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Iran

2 Department of Aerospace Engineering Amirkabir University of Technology (Tehran Polytechnic)

Abstract

In this paper, the effects caused by the combination of folding angles simultaneously with changing the stiffness ratio of different parts of a folding wing are investigated. The geometrically exact fully intrinsic equations are employed to simulated the wing nonlinear dynamic behavior. The important advantages of these geometrically exact equations can be seen as complete modeling without simplifying assumptions in large deformations, low-order nonlinearities, and thus less complexity. In this research, folding angles have been used in the geometrically exact fully intrinsic beam equations and the combination of different folding angles is studied. The applied aerodynamic loads in an incompressible flow regime are determined employing Peter’s unsteady aerodynamic model. In order to check the stability of the system, first the resulting non-linear partial differential equations are discretized, and then linearized about the nonlinear steady-state condition. By obtaining the eigenvalues of the linearized system, the stability of the wing is evaluated. Furthermore, investigation of the effects of the stiffness on the flutter speed and frequency of the folding wing for various folding angles, is another achievement of this study. It is observed that the combination of folding angles can significantly delay the flutter speed and improve the performance of the bird.

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###### ##### References
[1] D. H. Lee and P. Chen, "Nonlinear aeroelastic studies on a folding wing configuration with free-play hinge nonlinearity," in 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 14th AIAA/ASME/AHS Adaptive Structures Conference 7th, 2006, p. 1734.
[2] N. Ameri, M. Lowenberg, and M. Friswell, "Modelling the dynamic response of a morphing wing with active winglets," in AIAA Atmospheric Flight Mechanics Conference and Exhibit, 2007, p. 6500.
[3] D. Tang and E. H. Dowell, "Theoretical and experimental aeroelastic study for folding wing structures," Journal of Aircraft, vol. 45, pp. 1136-1147, 2008.
[4] P. J. Attar, D. Tang, and E. H. Dowell, "Nonlinear aeroelastic study for folding wing structures," AIAA journal, vol. 48, pp. 2187-2195, 2010.
[5] S. Liska and E. H. Dowell, "Continuum aeroelastic model for a folding-wing configuration," AIAA Journal, vol. 47, pp. 2350-2358, 2009.
[6] Y. Zhao and H. Hu, "Parameterized aeroelastic modeling and flutter analysis for a folding wing," Journal of Sound and Vibration, vol. 331, pp. 308-324, 2012.
[7] R. M. Ajaj, E. I. Saavedra Flores, M. Amoozgar, and J. E. Cooper, "A Parametric Study on the Aeroelasticity of Flared Hinge Folding Wingtips," Aerospace, vol. 8, p. 221, 2021.
[8] S. H. Moravej Barzani and H. Shahverdi, "Nonlinear aeroelastic stability analysis of a folding wing by using geometrically exact fully intrinsic beam equations," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, p. 09544100231167728, 2023.
[9] G. Hegemier and S. Nair, "A nonlinear dynamical theory for heterogeneous, anisotropic, elasticrods," AIAA Journal, vol. 15, pp. 8-15, 1977.
[10] D. H. Hodges, "Geometrically exact, intrinsic theory for dynamics of curved and twisted anisotropic beams," AIAA journal, vol. 41, pp. 1131-1137, 2003.
[11] Z. Sotoudeh and D. Hodges, "Parametric study of joined-wing aircraft geometry," in 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 18th AIAA/ASME/AHS Adaptive Structures Conference 12th, 2010, p. 2718.
[12] H. Moravej Barzani, M. Amoozgar, and H. Shahverdi, "Flutter Instability of Aircraft Swept Wings by Using Fully Intrinsic Equations," Persian, Amirkabir Journal of Mechanical Engineering, vol. 49, pp. 275-278, 2018.
[13] M. Amoozgar, S. A. Fazelzadeh, M. I. Friswell, and D. H. Hodges, "Aeroelastic stability analysis of tailored pretwisted wings," AIAA Journal, vol. 57, pp. 4458-4466, 2019.
[14] S. H. Moravej Barzani, H. Shahverdi, and M. Amoozgar, "Nonlinear aeroelastic stability analysis of a two-stage axially moving telescopic wing by using fully intrinsic equations," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, p. 09544100221080117, 2022.
[15] C.-S. Chang, "Vibration and aeroelastic analysis of highly flexible HALE aircraft," Georgia Institute of Technology, 2006.
[16] D. A. Peters, S. Karunamoorthy, and W.-M. Cao, "Finite state induced flow models. I-Two-dimensional thin airfoil," Journal of aircraft, vol. 32, pp. 313-322, 1995.
[17] N. Nguyen and I. Tuzcu, "Flight dynamics of flexible aircraft with aeroelastic and inertial force interactions," in AIAA atmospheric flight mechanics conference, 2009, p. 6045.
[18] M. J. Patil, "Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft," Georgia Institute of Technology, 1999.