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A note on typographical errors defining Theodorsen’s coefficients for aeroelastic analysis. (English) Zbl 1400.74022

Summary: The problem of flutter is an important topic involving aeroelastic analysis. The first approach to studying this problem was proposed by Theodore Theodorsen in [“General theory of aerodynamic instability and the mechanics of flutter”, NACA Report 496 (1935)] and, since that publication, Theodorsen’s theory has been extensively used by many researchers. However, it is common to find typographical errors in the definitions of the coefficients introduced by Theodorsen to determine the aerodynamic forces in a typical section airfoil. In this context, this paper summarizes the most common typographical errors found in the literature and includes mathematical demonstrations to clarify the correct form of those coefficients.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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References:

[1] Abdelkefi, A, Vasconcellos, R, Marques, FD (2012) Bifurcation analysis of an aeroelastic system with concentrated nonlinearities. Nonlinear Dynamics 69: 57-70. · Zbl 1296.70020
[2] Alighanbari H (1995) Flutter analysis and chaotic response of an airfoil accounting for structural nonlinearities. PhD Thesis, McGill University, Canada.
[3] Bisplinghoff, R, Ashley, H (1962) Principles of Aeroelasticity, New York: Wiley. · Zbl 0114.19802
[4] Bueno, DD, Góes, LCS, Gonçalves, PJP (2014) Control of limit cycle oscillation in a three degrees of freedom airfoil section using fuzzy Takagi-Sugeno modeling. Shock and Vibration 2014: 1-12.
[5] Dowell, EH, Crawley, EF, Curtiss, HC (1995) A Modern Course in Aeroelasticity, Dordrecht: Kluwer Academic Publishers.
[6] Edwards, J, Ashley, H, Breakwell, J (1979) Unsteady aerodynamic modeling for arbitrary motions. AIAA Journal 17(4): 365-374. · Zbl 0396.76004
[7] Hodges, DH, Pierce, GA (2002) Introduction to Structural Dynamic and Aeroelasticity, New York: Cambridge University Press.
[8] Kanda, A, Dowell, EH (2005) Worst-case gust-response analysis for typical airfoil section with control surface. Journal of Aircraft 42(4): 956-962.
[9] Karpel M (1981) Design for active and passive flutter suppression and gust alleviation. Report no. TR 3482, National Aeronautics and Space Administration, Washington DC.
[10] Ko J, Strganac TW, and Kurdila AJ (1998) Nonlinear adaptive control of an aeroelastic system via geometric methods. In: 39th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and material conference, Long Beach, CA, 20-23 April 1998, pp.98-1795. Reston, VA: AIAA.
[11] Li, D, Guo, S, Xiang, J (2010) Aeroelastic dynamic response and control of an airfoil section with control surface nonlinearities. Journal of Sound and Vibration 329(22): 4756-4771.
[12] Perry B (2015) Re-computation of numerical results contained in NACA report no. 496. Technical report, NASA Langley Research Center, Hampton, VA.
[13] Perry, B (2016) Results of national advisory committee for aeronautics report number 496: revisited. Journal of Aircraft 53(5): 1561-1565.
[14] Theodorsen T (1935) General theory of aerodynamic instability and the mechanism of flutter. NACA report no 496. · JFM 60.1397.05
[15] Vasconcellos, R, Abdelkefi, A, Marques, FD (2012) Representation and analysis of control surface freeplay nonlinearity. Journal of Fluids and Structures 31: 79-91.
[16] Wright, JR, Cooper, JE (2007) Introduction to Aircraft Aeroelasticity and Loads, Chichester: John Wiley & Sons, Ltd.
[17] Zeiler, TA (2000) Results of Theodorsen and Garrick revisited. Journal of Aircraft 37(5): 918-920.
[18] Zhang, K, Behal, A (2016) Continuous robust control for aeroelastic vibration control of a 2-D airfoil under unsteady flow. Journal of Vibration and Control 22(12): 2841-28620. · Zbl 1365.93211
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