A modified indicial functions approximation for nonlinear aeroelastic analysis

Document Type : Article

Authors

1 Department of Aerospace Engineering, Malek-Ashtar University of Technology, Tehran, Iran

2 Department of Aerospace Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

Abstract

The nonlinear dynamic response, Limit Cycle Oscillations (LCOs), of high aspect ratio wings using a novel indicial aerodynamics in subsonic flow is investigated. Using the nonlinear beam theory, the structural model is derived including the in-plane and out-of-plane bending and torsion motions, all nonlinearities up to cubic order arising from large deformation, mass distribution, and cross-sectional mass imbalance. Based on new approximations of the indicial functions, a comprehensive unsteady aerodynamic model is used. Such an indicial aerodynamics while being coupled to nonlinear structural equations can result in a unified nonlinear aeroelastic formulation in both the incompressible and subsonic compressible flow. The effect of flight conditions, wing tip initial disturbances, stiffness ratio between bending modes, and nonlinearity due to inertia and cross-sectional mass imbalance on the characteristics of LCO are discussed. The results show that the compressibility can affect the LCO boundary up to 12 percent which implies that an appropriate Mach-dependent aerodynamics is required to achieve a more reasonable and realistic description of dynamic behavior of the system. It is shown that the presence of LCO before the linear flutter speed depends on initial disturbances as well as wing characteristics.

Keywords

Main Subjects

References

References:
1. Xiang, J., Yan, Y., and Li, D. "Recent advance in nonlinear aeroelastic analysis and control of the aircraft", Chinese Journal of Aeronautics, 27(1), pp. 12-22 (2014). DOI: 10.1016/j.cja.2013.12.009.
2. Nayfeh, A.H. and Pai, P.F., Linear and Nonlinear Structural Mechanics, pp. 171-266, John Wiley & Sons, Germany (2004).
3. Patil, M.J., Hodges, D.H., and Cesnik, C.E. "Limitcycle oscillations in high-aspect-ratio wings", Journal of Fluids and Structures, 15(1), pp. 107-132 (2001). DOI: 10.1006/j s.2000.0329. 
4. Strganac, T., Cizmas, P., Nichkawde, C., et al. "Aeroelastic analysis for future air vehicle concepts using a fully nonlinear methodology", 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Austin, Texas (2005).
5. Hodges, D.H. and Dowell, E. "Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades", NASA TN D-7818 (1974).
6. Dowell, E., Traybar, J., and Hodges, D.H. "An experimental-theoretical correlation study of nonlinear bending and torsion deformations of a cantilever beam", Journal of Sound and Vibration, 50(4), pp. 533-544 (1977). DOI: 10.1016/0022-460X(77)90501-6.
7. Rosen, A. and Friedmann, P. "The nonlinear behavior of elastic slender straight beams undergoing small strains and moderate rotations", Journal of Applied Mechanics, 46(1), pp. 161-168 (1979). DOI: 10.1115/1.3424490.
8. Crespo da Silva, M. and Glynn, C. "Nonlinear flexural-flexural-torsional dynamics of inextensional beams. I. Equations of motion", Journal of Structural Mechanics, 6(4), pp. 437-448 (1978). DOI:10.1080/03601217808907348.
9. Pai, P.F. and Nayfeh, A. H. "Three-dimensional nonlinear vibrations of composite beams-I. Equations of motion", Nonlinear Dynamics, 1(6), pp. 477-502 (1990). DOI: 10.1007/BF01856950.
10. Nayfeh, A.H. and Pai, P.F. "Non-linear non-planar parametric responses of an inextensional beam", International Journal of Non-Linear Mechanics, 24(2), pp. 139-158 (1989). DOI: 10.1016/0020-7462(89)90005-X.
11. Hodges, D.H. "A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams", International Journal of Solids and Structures, 26(11), pp. 1253-1273 (1990).
12. Bakhtiarinezhad, F. and Shokrollahi, S. "Threedimensional eigenmode  utter analysis of a rectangular cantilever plate in low subsonic fl ow", Scientia Iranica, 11(1-2), pp. 60-68 (2004).
13. Katz, J. and Plotkin, A., Low-speed Aerodynamics, 13, Cambridge university press (2001).
14. Kier, T.M. "Comparison of unsteady aerodynamic modelling methodologies with respect to  flight loads analysis", In Proceedings of the AIAA Atmospheric Flight Mechanics Conference and Exhibit (2005).
15. Leishman, J. "Validation of approximate indicial aerodynamic functions for two-dimensional subsonic flow", Journal of Aircraft, 25(10), pp. 914-922 (1988). DOI: 10.2514/3.45680.
16. Marzocca, P., Librescu, L., and Chiocchia, G. "Unsteady aerodynamics in various  flight speed regimes for  flutter/dynamic response analyses", In 18th AIAA Applied Aerodynamic Conference, AIAA 2000-4229, Denver, CO, pp. 491-501 (2000).
17. Murua, J., Palacios, R., and Graham, J.M.R. "Applications of the unsteady vortex-lattice method in aircraft aeroelasticity and  flight dynamics", Progress in Aerospace Sciences, 55, pp. 46-72 (2012).
18. Mazelsky, B. "Numerical determination of indicial lift of a two-dimensional sinking airfoil at subsonic Mach numbers from oscillatory lift coefficients with calculations for Mach number 0.7", NACA TN 2562 (1951).
19. Mazelsky, B. "Determination of indicial lift and moment of a two-dimensional pitching airfoil at subsonic Mach numbers from oscillatory coefficients with numerical calculations for a Mach number of 0.7", NACA TN 2613 (1952).
20. Mazelsky, B. and Drischler, J.A. "Numerical determination of indicial lift and moment functions for a two-dimensional sinking and pitching airfoil at Mach numbers 0.5 and 0.6", NACA TN 2739 (1952).
21. Marzocca, P., Librescu, L., and Chiocchia, G. "Aeroelastic response of a 2-D airfoil in a compressible flow field and exposed to blast loading", Aerospace Science and Technology, 6(4), pp. 259-272 (2002). DOI: 10.1016/S1270-9638(02)01169-0.
22. Marzocca, P., Librescu, L., Kim, D., et al. "Development of an indicial function approach for the two-dimensional incompressible/compressible aerodynamic load modelling", Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 221(3), pp. 453-463 (2007). DOI: 10.1243/09544100JAERO88.
23. Farsadi, T. and Javanshir, J. "Expansion of indicial function approximations for 2-D subsonic compressible aerodynamic loads", In Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition, Houstoun, Texas, pp. 519-528 (2012).
24. Nejati, M., Shokrollahi, S., and Shams, S. "A comprehensive model to compute incompressible-subsonic compressible unsteady aerodynamic loads using indicial functions", Modares Mechanical Engineering, 17(1), pp. 353-364 (in Persian) (2017).
25. Nejati, M., Shokrollahi, S., and Shams, S. "Nonlinear aeroelastic analysis of high-aspect-ratio wings using indicial aerodynamics", Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(6), p. 298 (2018).
26. Bisplinghoff, R.L., Ashley, H., and Halfman, R.L., Aeroelasticity, pp. 323-353, Dover Publications, New York (1996).
27. Qin, Z. and Librescu, L. "Aeroelastic instability of aircraft wings modelled as anisotropic composite thinwalled beams in incompressible  flow", Journal of Fluids and Structures, 18(1), pp. 43-61 (2003). DOI:10.1016/S0889-9746(03)00082-3.
28. Tang, D. and Dowell, E.H. "Experimental and theoretical study on aeroelastic response of high-aspect-ratio wings", AIAA Journal, 39(8), pp. 1430-1441 (2001). DOI: 10.2514/2.1484.
29. Shams, S., Lahidjani, M.S., and Haddadpour, H. "Nonlinear aeroelastic response of slender wings based on Wagner function", Thin-Walled Structures, 46(11), pp. 1192-1203 (2008). DOI: 10.1016/j.tws.2008.03.001.
30. Shams, S., Sadr, M., and Haddadpour, H. "An efficient method for nonlinear aeroelasticy of slender wings", Nonlinear Dynamics, 67(1), pp. 659-681 (2012). DOI: 10.1007/s11071-011-0018-2.
31. Jian, Z. and Jinwu, X. "Nonlinear aeroelastic response of high-aspect-ratio flexible wings", Chinese Journal of Aeronautics, 22(4), pp. 355-363 (2009). DOI: 10.1016/S1000-9361(08)60111-9.
32. Hodges, D.H. "Geometrically exact, intrinsic theory for dynamics of curved and twisted anisotropic beams", AIAA Journal, 41(6), pp. 1131-1137 (2003). DOI: 10.2514/2.2054.
33. Eskandary, K., Dardel, M., Pashaei, M., et al. "Nonlinear aeroelastic analysis of high-aspect-ratio wings in low subsonic  flow", Acta Astronautica, 70, pp. 6-22 (2012). DOI: 10.1016/j.actaastro.2011.07.017.
34. Badiei, D., Sadr, M., and Shams, S. "Static stall model in aeroelastic analysis of a  flexible wing with geometrical nonlinearity", Journal of Aerospace Engineering, 27(2), pp. 378-389 (2012). DOI: 10.1061/(ASCE) AS.1943-5525.0000263.
35. Dardel, M., Eskandary, K., Pashaei, M., et al. "The effect of angle of attack on limit cycle oscillations for high-aspect-ratio wings", Scientia Iranica, Transactions B, Mechanical Engineering, 21(1), p. 130 (2014).
36. Xiao, Y.P., Yang, Y.R., and Li, P. "Limit-cycle oscillation of high-aspect-ratio wings", Applied Mechanics and Materials, 556-562, pp. 4329-4332, (2014). DOI: 10.4028/www.scientific.net/AMM.556-562.4329.
37. Koohi, R., Shahverdi, H., and Haddadpour, H. "Nonlinear aeroelastic analysis of a composite wing by finite element method", Composite Structures, 113, pp. 118- 126 (2014).
38. Koohi, R., Shahverdi, H., and Haddadpour, H. "Modal and aeroelastic analysis of a high-aspect-ratio wing with large deflection capability", International Journal Advanced Design and Manufacturing Technology, 8(1), pp. 45-54 (2015).
39. Yuan, K.A. and Friedmann, P.P. "Aeroelasticity and structural optimization of composite helicopter rotor blades with swept tips", National Aeronautics and Space Administration, Langley Research Center NASA CR, 4665 (1995).
40. Jung, Y.S., Yu, D.O., and Kwon, O.J. "Aeroelastic analysis of high-aspect-ratio wings using a coupled CFD-CSD method", Transactions of the Japan Society for Aeronautical and Space Sciences, 59(3), pp. 123- 133 (2016).
41. Bakhtiari-Nejad, F., Modarres, A., Dowell, E., et al. "Linear and nonlinear aeroelastic analysis of a high aspect ratio wing", In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Cleveland, Ohio (2017).
42. Hoseini, H. and Hodges, D.H. "Aeroelastic analysis of high aspect ratio wings using joined 3D finite elements and variational asymptotic beam models," 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Grapevine, Texas (2017).
43. Farsadi, T., Rahmanian, M., and Kayran, A. "Geometrically nonlinear aeroelastic behavior of pretwisted composite wings modeled as thin walled beams", Journal of Fluids and Structures, 83, pp. 259-292 (2018).
44. Xu, Y., Cao, D., Lin, H., et al. "An alternative simulation approach for the ONERA aerodynamic model and its application in the nonlinear aeroelastic analysis of slender wings with pylon-store system", International Journal of Non-Linear Mechanics, 105, pp. 55-76 (2018).
45. Abbas, L., Chen, Q., Marzocca, P., et al. "Nonlinear aeroelastic investigations of store (s)-induced limit cycle oscillations", Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 222(1), pp. 63-80 (2008). DOI: 10.1243/09544100JAERO241.
46. Sina, S., Farsadi, T., and Haddadpour, H. "Aeroelastic stability and response of composite swept wings in subsonic flow using indicial aerodynamics", Journal of Vibration and Acoustics, 135(5), p. 051019 (2013). DOI: 10.1115/1.4023992.
47. Wright, J.R. and Cooper, J.E., Introduction to Aircraft Aeroelasticity and Loads, 20, pp. 76-80, John Wiley & Sons, England (2008).
48. Rao, S.S., Vibration of Continuous Systems, pp. 333- 335, John Wiley & Sons, United States of America (2007).
49. Fazelzadeh, S., Marzocca, P., Rashidi, E., et al. "Effects of rolling maneuver on divergence and  flutter of aircraft wing store", Journal of Aircraft, 47(1), pp. 64-70 (2010). DOI: 10.2514/1.40463.
50. Clark, R., Cox, D., Howard Jr, C., et al., A Modern Course in Aeroelasticity, 116, Springer Science & Business Media (2006).
51. Goland, M. "The  flutter of a uniform cantilever wing", Journal of Applied Mechanics-Transactions of the ASME, 12(4), pp. A197-A208 (1945).
52. Gern, F.H. and Librescu, L. "Effects of externally mounted stores on aeroelasticity of advanced swept cantilevered aircraft wings", Aerospace Science and Technology, 2(5), pp. 321-333 (1998). DOI:10.1016/S1270-9638(98)80008-4. 
53. Patil, M., Hodges, D., and Cesnik, C. "Nonlinear aeroelastic analysis of aircraft with high-aspectratio wings", in Proceeding of 39th AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA paper 98-1955, Long Beach, CA (1998).
Scientia Iranica
Volume 27, Issue 3
Transactions on Mechanical Engineering (B)
May and June 2020
Pages 1230-1254

Files

History

  • Receive Date: 06 January 2018
  • Revise Date: 30 October 2018
  • Accept Date: 26 January 2019

Share

How to cite

Statistics