Geometrically nonlinear effects in wing aeroelastic dynamics at large deflections

Abstract

This paper investigates geometrically nonlinear effects due to nonlinear kinematics and follower aerodynamics in the aeroelastic dynamics of a very flexible wing. The test case is the Pazy wing, a benchmark wing model for geometrically nonlinear aeroelastic studies involving large deflections in low-speed flow. The work builds on a low-order model of the wing composed of a geometrically nonlinear beam coupled with potential flow thin airfoil theory. Nonfollower aerodynamics underestimates static deflections by up to 10%, whereas linear kinematics overestimates them by up to 50%. At low static deflections, the wing hump mode flutter mechanism is driven by three-dimensional unsteady aerodynamic effects. As static deflections increase, the flutter onset and offset speeds are driven by curvature effects that can only be captured by nonlinear kinematics, which reduce the natural frequencies associated with torsion and in-plane bending motions. Follower aerodynamics shrinks the hump mode instability region and shifts it to 1–4% lower flow speeds with no change in the flutter frequency, the qualitative trends, and the amplitude of limit-cycle oscillations. Overall, nonlinear kinematics is the primary geometrical nonlinearity influencing the wing aeroelastic behavior: the modal and stability scenarios with and without follower aerodynamics collapse onto the same curves when presented as functions of the tip deflection. However, geometrical nonlinearities alone miss the subcritical nature of the hump mode flutter mechanism, which is attributed to aerodynamic stall and its interaction with large deflections. This work expands the growing literature on the aeroelastic dynamics of very flexible wings and will ease future studies considering aerodynamic nonlinear effects.