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Research Papers

Nonlinear Aeroelastic Analysis of Bending-Torsion Wings Subjected to a Transverse Follower Force

[+] Author and Article Information
S. A. Fazelzadeh1

Department of Mechanical Engineering, Shiraz University, Shiraz 89138, Iranfazelzad@shirazu.ac.ir

A. Mazidi

Department of Mechanical Engineering, Shiraz University, Shiraz 89138, Iranamazidi@shirazu.ac.ir

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(3), 031016 (Mar 02, 2011) (8 pages) doi:10.1115/1.4003288 History: Received January 11, 2010; Revised December 17, 2010; Published March 02, 2011; Online March 02, 2011

This paper deals with the nonlinear aeroelastic behaviors of bending-torsion wings subjected to a transverse follower force. The nonlinear structural wing formulation is based on von Karman large deformation theory. In order to accurately consider the spanwise location of the follower force, the generalized function theory is used. Also, Peter’s finite-state unsteady aerodynamic model is considered. The governing equations are obtained using Hamilton’s principle. Furthermore, the Galerkin method is applied to convert the partial differential equations into a set of nonlinear ordinary differential equations, which will be solved through the numerical integration scheme. Wing dynamic behaviors are investigated through frequency spectra and the bifurcation diagrams of Poincaré maps. In addition, the postcritical region, which includes all periodic, quasiperiodic, and chaotic pockets, is indeed found to exist. Furthermore, the results indicate noticeable effects of the follower force magnitude and location as well as the air stream velocity on critical and postcritical behaviors of a wing.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Nomenclature of a wing with follower force. (b) Deformed and undeformed wing coordinate systems. (c) The wing cross-section before and after deformation.

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Figure 2

Spectrum of the responses of the wing tip motion with p=4 for periodic, quasiperiodic, and chaotic behaviors, respectively, at flutter regions: (a) v∞=1.5, (b) v∞=1.7, and (c) v∞=2.3

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Figure 3

Bifurcation diagram of Poincaré maps of wing tip deflection with increasing air stream velocity for selected follower force locations with p=4: (a) xp=8 and (b) xp=15

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Figure 4

Bifurcation diagram of Poincaré maps of wing tip deflection with increasing air stream velocity for selected follower forces applied at xp=15: (a) p=0 and (b) p=6

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Figure 5

Critical and postcritical boundaries and regions of the wing subjected to a follower force applied at xp=15

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