Investigation of Geometrically Nonlinear Effects in the Aeroelastic Behavior of a Very Flexible Wing

Abstract

This paper investigates geometrically nonlinear effects associated with nonlinear kinematics and follower aerodynamics in the aeroelastic behavior of a very flexible wing in low-speed flow. The test case is the Pazy wing, a benchmark model for geometrically nonlinear studies developed under the Third Aeroelastic Prediction Workshop Large Deflection Working Group. The work builds on a validated low-order model of the Pazy wing that consists of a geometrically nonlinear beam coupled with potential flow thin airfoil theory. Neglecting follower aerodynamics underestimates static deflections by up to 10% while neglecting nonlinear kinematics overestimates them by up to 50%. As deflections increase, curvature effects captured by nonlinear kinematics decrease the natural frequencies associated with torsion and in-plane bending motions, reducing the onset and offset speeds of the wing hump mode flutter mechanism. Neglecting follower aerodynamics widens the hump mode instability region and shifts it at 1–4% higher flow speeds but does not change the flutter frequency and amplitude of post-flutter dynamics. Overall, nonlinear kinematics is the primary geometrical nonlinearity influencing the wing aeroelastic behavior. While follower aerodynamics effects change the deformed shape for a given operating condition, natural frequencies and aeroelastic eigenvalues with and without these effects evolve along the same curves once plotted with the flow speed as an implicit parameter. These results will aid future studies in very flexible wings including other nonlinearities such as stall.