Limit cycle oscillations in swept wings based on fully intrinsic equations and considering the static stall effects

Authors

1 Amirkabir Univ.

2 Amirkabir Univ

3 Amirkabir univ.

Abstract

In this paper, the dynamic instability of swept wings by using the geometrically exact fully intrinsic beam equations and with considering the static stall effects is investigated. Study of variations of the limit cycle amplitudes by using the fully intrinsic beam equations and ONERA unsteady aerodynamic model with static stall effects in swept wings is the achievement of this article. the geometrically exact fully intrinsic beam equations involve only moments, forces, velocity and angular velocity, and in these equations, the displacements and rotations will not appear explicitly. In this study, the aerodynamic loads on the wing in an incompressible flow regime are determined by using the ONERA unsteady aerodynamic model. In order to check the instability behavior of the system, first the resulting non-linear partial differential equations are discretized by using the central finite difference method, and then time responses are obtained. The obtained results are compared with those available in the literature. Furthermore, the effects of sweep angle are studied. Finally, it is observed that by using the geometrically exact fully intrinsic beam equations, the instability of the swept wings can be determined accurately and selection of suitable sweep angle can postpone the occurrence of limit cycle oscillation.

Keywords

References

[[1]] Hodges DH, Dowell EH (1974) Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades. (No. Naca-A-5711(.
[2] Arafat HN (1999) Nonlinear response of cantilever beams. Doctoral Dissertation, Virginia Polytechnic Institute and State University.
[3] Hodges DH (2003) Geometrically exact intrinsic theory for dynamics of curved and twisted anisotropic beams. AIAA J 41(6): 1131-1137.
 [4] Reissner E (1973) On one-dimensional large-displacement finite-strain beam theory. Stud Appl Math 52(2): 87-95.
[5] Hegemier GA, Nair S (1977) A nonlinear dynamical theory for heterogeneous anisotropic elastic rods. AIAA J 15(1): 8-15.
[6] Hodges DH, Shang X, Cesnik CE (1996) Finite element solution of nonlinear intrinsic equations for curved composite beams. J Am Helicopter Soc 41(4): 313-321.
[7] Patil MJ, Hodges DH (2006) Flight dynamics of highly flexible flying wings. J Aircraft 43(6): 1790-1799.
[8] Chang CS, Hodges D (2009) Vibration characteristics of curved beams. J Mech Mater Struct 4(4): 675-692.
[9] Sotoudeh Z, Hodges DH (2009) Nonlinear aeroelastic analysis of joined-wing aircraft with intrinsic equations. In 50th Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA, AIAA Paper.
[[1]0] Shams S, Lahidjani MS, Haddadpour H (2008) Nonlinear aeroelastic response of slender wings based on Wagner function. Thin Wall Struct, 46(11): 1192-1203.
[1[1]] Dunn P, Dugundji J (1992) Nonlinear stall and divergence analysis of cantilevered graphite/epoxy wing. AIAA J 30(1): 153-162.
[12] Tang D, Dowell EH (2001) Experimental and theoretical study on aeroelastic response of high-aspect-ratio wings. AIAA J 39(8): 1430-1441.
[[1]3] Jian Z, Jinwu X (2009) Nonlinear aeroelastic response of high-aspect-ratio flexible wings. Chinese J Aeronaut 22(4): 355-363.
[[1]4] Patil MJ (1999) Nonlinear aeroelastic analysis flight dynamics and control of a complete aircraft. Georgia Institute of Technology.
[[1]5] Barmby JG, Cunningham HJ, Garrick IE (1950) Study of effects of sweep on the flutter of cantilever wings. (No. Naca-TR-1014).
[[1]6] Molyneux WG, Hall H (1957) The aerodynamics effects of aspect ratio and sweepback on wing flutter. (A.R.C-TR).
[[1]7] Lottati I (1985) Flutter and divergence aeroelastic characteristics for composite forward swept cantilevered wing. J Aircraft 22(11): 1001-1007.
[[1]8] Karpouzian G, Librescu L (1996) Nonclassical effects on divergence and flutter of anisotropic swept aircraft wings. AIAA J 34(4): 786-794.
[[1]9] Mazidi A, Fazelzadeh SA (2010) Flutter of a swept aircraft wing with a powered engine. J Aerospace Eng 23(4): 243-250.
[20] مروج ح، آموزگار م، شاهوردی ح (1396) تحلیل ناپایداری فلاتر بال‌های دارای زاویه پس گرایی با استفاده از معادلات کاملاً ذاتی. نشریه مهندسی مکانیک امیرکبیر 794-785 :(4)49.
[2[1]] Amoozgar MR, Shahverdi H (2016) Analysis of nonlinear fully intrinsic equations of geometrically exact beams using generalized differential quadrature method. ACTA Mech 227(5): 1265-1277.
[22] Hodges DH (1990) A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams. Int J Solids Struct 26(11): 1253-1273.
[23] Beedy J, Barakos G (2002) Non-linear analysis of stall flutter based on the ONERA Aerodynamic model. Aerospace Engineering Report 0205b.
[24] O'Reilly OM (2008) Intermediate dynamics for engineers: a unified treatment of newton-euler and lagrangian mechanics. Cambridge University Press.
[25] Patil MJ, Hodges DH, Cesnik CE (2001) Limit-cycle oscillations in high-aspect-ratio wings. J Fluid Struct 15(1): 107-132.
[26] Chang CS (2006) Vibration and aeroelastic analysis of highly flexible HALE aircraft. Doctoral Dissertation, Georgia Institute of Technology.
Journal of Solid and Fluid Mechanics
Volume 11, Issue 6
January and February 2022
Pages 207-217

Files

Share

How to cite

Statistics