Aeroelastic Modeling of Deformable-Airfoil Wings Through Unsteady Lifting-Line Theory

This paper presents a state-space formulation for the aeroelastic stability analysis of deformable airfoil wings. The proposed approach couples the wing structural dynamics modeled as a cantilever plate (through an FEM approach) with aerodynamic loads computed through an Unsteady Lifting-Line Theory (ULLT), which evaluates the unsteady sectional loads using the Kussner-Schwarz theory and accounts for wake effects through the Biot–Savart law. The corresponding bound circulation is obtained via the Kutta–Joukowski theorem extended to unsteady flows. The distributed aerodynamic loads are projected onto the shape functions introduced in a Galerkin solution approach, thus yielding an aerodynamic operator expressed through transcendental transfer functions, which is then approximated into a rational state-space form. This enables straightforward aeroelastic stability assessment through eigenvalue analysis and provides a framework suitable for control design. The model’s accuracy is validated using the paper flutter problem, whose aeroelastic behavior is representative of deformable-airfoil wings.