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This paper presents a nonlinear aeroelastic formulation of a coupled bending-torsion motion of a onedimensional 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.

This paper presents a coupled vortex-lattice flight dynamic model with an aeroelastic finite-element model to predict dynamic characteristics of a flexible wing transport aircraft. The aircraft model is based on NASA Generic Transport Model (GTM) with representative mass and stiffness properties to achieve a wing tip deflection about twice that of a conventional transport aircraft (10% versus 5%). This flexible wing transport aircraft is referred to as an Elastically Shaped Aircraft Concept (ESAC) which is equipped with a new aerodynamic control surface for active wing shaping control for drag reduction. This aerodynamic surface is referred to as a Variable Camber Continuous Trailing Edge Flap (VCCTEF). A vortex-lattice aerodynamic model of the ESAC is developed for coupling with the aeroelastic finite-element model via an automated geometry generation tool. This coupled model is used to compute static and dynamic aeroelastic solutions. The deflection information from the finite-element model and the vortex-lattice model is used to compute unsteady contributions to the aerodynamic force and moment coefficients which are used for the flight dynamic model. Two different methods for a state-space formulation for coupled aeroelastic-flight dynamics are considered to address the dependency on the reduced frequency parameter. The first method is to formulate the equations of motion which are dependent on the exact Theodorsen's unsteady aerodynamic model. The second method is to approximate the Theodorsen's complex-valued function as a second-order transfer function proposed by R. T. Jones. This approximation eliminates the reduced frequency dependency, but also results into two additional states for each of the structural deflection state. Both methods will be described in the study. A vehicle stability analysis will be conducted to assess the effect of aeroelasticity on rigid-body aircraft modes.

This paper presents a coupled vortex-lattice flight dynamic model with an aeroelastic finite-element model to predict dynamic characteristics of a flexible wing transport aircraft. The aircraft model is based on NASA Generic Transport Model (GTM) with representative mass and stiffness properties to achieve a wing tip deflection about twice that of a conventional transport aircraft (10% versus 5%). This flexible wing transport aircraft is referred to as an Elastically Shaped Aircraft Concept (ESAC) which is equipped with a Variable Camber Continuous Trailing Edge Flap (VCCTEF) system for active wing shaping control for drag reduction. A vortex-lattice aerodynamic model of the ESAC is developed and is coupled with an aeroelastic finite-element model via an automated geometry modeler. This coupled model is used to compute static and dynamic aeroelastic solutions. The deflection information from the finite-element model and the vortex-lattice model is used to compute unsteady contributions to the aerodynamic force and moment coefficients. A coupled aeroelasticlongitudinal flight dynamic model is developed by coupling the finite-element model with the rigid-body flight dynamic model of the GTM.