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An analytical solution to the aeroelastic response of a two-dimensional elastic plate in axial potential flow

Published online by Cambridge University Press:  20 April 2018

Cory Medina  and
Chang-kwon Kang Open the ORCID record for Chang-kwon Kang [Opens in a new window]
Cory Medina
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA NASA Marshall Space Flight Center, Huntsville, AL 35812, USA
Chang-kwon Kang*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA
*
†Email address for correspondence: [email protected]
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Abstract

This paper presents a novel analytical model that predicts the two-way coupled aeroelastic response of a linear elastic plate in axial potential flow, including the effects of plate curvature. The plate deforms in dynamic balance of the inertia, elastic, and aerodynamic forces. Analytical solutions are obtained by deriving the generalized aerodynamic force with respect to the beam eigenfunctions, which are expressed in a Chebyshev polynomial expansion. Exact expressions are derived for the generated lift, thrust and required input power. The derived solution agrees well with the results reported in the literature for plate flutter and flapping wings.

JFM classification

Aerodynamics: Aerodynamics Biological Fluid Dynamics: Swimming/flying
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 845 , 25 June 2018 , R3
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Copyright
© Cambridge University Press 2018. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

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References

Bisplinghoff, R. L., Ashley, H. & Halfman, R. L. 1996 Aeroelasticity. Dover Publications.Google Scholar
Breuker, R. D., Abdalla, M. M. & Gürdal, Z. 2008 Flutter of partially rigid cantilevered two-dimensional plates in axial flow. AIAA J. 46 (4), 936–946.CrossRefGoogle Scholar
Eloy, C., Lagrange, R., Souilliez, C. & Schouveiler, L. 2008 Aeroelastic instability of cantilevered flexible plates in uniform flow. J. Fluid Mech. 611, 97–106.Google Scholar
Glauert, H. 1926 The Elements of Aerofoil and Airscrew Theory. Cambridge University Press.Google Scholar
Guo, C. Q. & Païdoussis, M. P. 2000 Stability of rectangular plates with free side-edges in two-dimensional inviscid channel flow. Trans. ASME J. Appl. Mech. 67, 171–176.Google Scholar
Huang, L. 1995 Flutter of cantilevered plates in axial flow. J. Fluids Struct. 9 (2), 127–147.Google Scholar
Kang, C.-K., Aono, H., Cesnik, C. E. S. & Shyy, W. 2011 Effects of flexibility on the aerodynamic performance of flapping wings. J. Fluid Mech. 689, 32–74.Google Scholar
von Karman, T. & Burgers, J. M. 1935 General Aerodynamic Theory – Perfect Fluids (ed. Durand, W. F.), Aerodynamic Theory, vol. 2, pp. 1–24. Springer.Google Scholar
Katz, J. & Plotkin, A. 2001 Low-Speed Aerodynamics, 2nd edn.. Cambridge University Press.Google Scholar
Kornecki, A., Dowell, E. H. & O’Brien, J. 1976 On the aeroelastic instability of two-dimensional panels in uniform incompressible flow. J. Sound Vib. 47 (2), 163–178.Google Scholar
Küssner, H. G. & Schwarz, I.1941 The oscillating wing with aerodynamically balanced elevator. Tech. Rep. No. 991. National Advisory Committee for Aeronautics.Google Scholar
Landahl, M. T. & Stark, V. J. E. 1968 Numerical lifting-surface theory – problems and progress. AIAA J. 6 (11), 2049–2060.Google Scholar
Moore, M. N. J. 2017 A fast chebyshev method for simulating flexible-wing propulsion. J. Comput. Phys. 345, 792–817.Google Scholar
Shelley, M. J. & Zhang, J. 2011 Flapping and bending bodies interacting with fluid flows. Annu. Rev. Fluid Mech. 43, 449–465.Google Scholar
Theodorsen, T.1935 General theory of aerodynamic instability and the mechanism of flutter. Tech. Rep. No. 496. National Advisory Committee for Aeronautics.Google Scholar
Timoshenko, S. P. 2017 Vibration Problems in Engineering, 5th edn. Dead Authors Society.Google Scholar
Walker, W. P. & Patil, M. J. 2014 Unsteady aerodynamics of deformable thin airfoils. J. Aircraft 51 (6), 1673–1680.Google Scholar
Watanabe, Y., Isaogai, K., Suzuki, S. & Sugihara, M. 2002 A theoretical study of paper flutter. J. Fluids Struct. 16 (4), 543–560.Google Scholar
Watkins, C. E., Woolston, D. S. & Cunningham, H. J.1959 A systematic kernel function procedure for determining aerodynamic forces on oscillating or steady finite wings at subsonic speeds. Tech. Rep. No. 48. National Aeronautics and Space Administration.Google Scholar
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