Static Stall Model in Aeroelastic Analysis of a Flexible Wing with Geometrical Nonlinearity

Abstract

This paper presents the nonlinear aeroelastic analysis of slender wings using a nonlinear structural model coupled with a nonlinear unsteady aerodynamic model. A high-aspect ratio and flexibility are the specific characteristics of this type of wing. Wing flexibility, coupled with a 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 flexible Euler-Bernoulli beam equations is used for the structural modeling. An unsteady nonlinear aerodynamic considering static stall based on the Wagner function is used for determination of aerodynamic loading of the wing. Combining these two types of formulations yields fully nonlinear integro/differential aeroelastic equations. Using Galerkin’s method, a mode summation technique, and a numerical method, the governing equations are solved to predict the nonlinear aeroelastic response of a wing in the stall region. The results obtained are compared with the results given in the literature. In addition, the effects of the static stall characteristics of some typical airfoils on the aeroelastic behavior of a flexible wing are investigated. The results indicate that in a range of static stall angles of attacks there is a specific angle of attack in which the limit cycle oscillation boundary speed has a maximum value.