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An efficient method for nonlinear aeroelasticy of slender wings

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Abstract

This paper aims the nonlinear aeroelastic analysis of slender wings using a nonlinear structural model coupled with the linear unsteady aerodynamic model. High aspect ratio and flexibility are the specific characteristic of this type of wings. Wing flexibility, coupled with long wingspan can lead to large deflections during normal flight operation of an aircraft; therefore, a wing in vertical/forward-afterward/torsional motion using a third-order form of nonlinear general flexible Euler–Bernoulli beam equations is used for structural modeling. Unsteady linear aerodynamic strip theory based on the Wagner function is used for determination of aerodynamic loading on the wing. Combining these two types of formulation yields nonlinear integro-differentials aeroelastic equations. Using the Galerkin’s method and a mode summation technique, the governing equations will be solved by introducing a numerical method without the need to adding any aerodynamic state space variables and the corresponding equations related to these variables of the problem. The obtained equations are solved to predict the aeroelastic response of the problem. The obtained results for a test case are compared with those of some other works and show a good agreement between results.

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Abbreviations

x,y,z :

Undeformed coordinates system

v,w,θ :

Forward, vertical, and torsional motions

U,ρ :

Air speed and density of free stream

l,c,b :

Length, chord, and half-chord of wing

m,S α ,J α :

Mass per length, first and second moment of inertia per mass of wing

L,M e.a :

Lift and pitching moment distribution about elastic axis

a,x θ :

Distance coefficient of mid chord and center of gravity to elastic axis

ξ,η,ζ:

Deformed coordinates system

EI,GJ :

Bending and torsional stiffness

ϕ(t):

Wagner function

ξ i ,η i ,β i :

Generalized coordinates

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Authors and Affiliations

  1. Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran

    S. Shams & M. H. Sadr

  2. Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran

    H. Haddadpour

Authors
  1. S. Shams
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  2. M. H. Sadr
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  3. H. Haddadpour
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Correspondence to H. Haddadpour.

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Shams, S., Sadr, M.H. & Haddadpour, H. An efficient method for nonlinear aeroelasticy of slender wings. Nonlinear Dyn 67, 659–681 (2012). https://doi.org/10.1007/s11071-011-0018-2

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  • DOI: https://doi.org/10.1007/s11071-011-0018-2

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