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

Abstract

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.