This paper presents a nonlinear aeroelastic formulation of a coupled bending-torsion motion of a one-dimensional flexible wing structure that is fully coupled with an aircraft rigid-body motion. The aeroelastic angle of attack is derived from kinematics of aircraft rigid-body velocities and wing aeroelastic deflection velocities. The nonlinear aeroelastic formulation fully takes into account engine thrust forces which are coupled with aeroelasticity, and wing pre-twist and dihedral angles which can increase the degree of coupling between the wing aeroelastic deflections and the aircraft rigid-body motion. The nonlinear aeroelastic deflection effects result in a nonlinear aerodynamic damping. A finite-element analysis method is used to discretize the nonlinear aeroelastic equations of the coupled bending-torsion motion. Static aeroelastic analysis is performed by coupling the finite-element model with a vortex-lattice aerodynamic model of an aircraft. A modal analysis based on the quasi-steady state aerodynamic assumption is conducted to compute aeroelastic symmetric modes and anti-symmetric modes of the wing structure. All aeroelastic modes are found to be stable within a flight envelope. The first two flutter airspeeds are due to the symmetric third bending mode and the anti-symmetric second bending mode, both of which occur well above the flight envelope of the generic transport aircraft. The nonlinear damping effect can contribute positively to the aerodynamic damping that can improve aeroelastic stability of a wing structure.
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