Nonlinear aeroelastic analysis of airfoils using a continuous-time state-space panel method with viscous effects

Conventional aerodynamic simulation methods in aeroelasticity struggle to ensure computational accuracy when handling complex geometries and viscous-dominated flow regimes. To address this limitation, this study develops a two-dimensional unsteady differential boundary layer equation solver and integrates it into an unsteady panel method framework. The discretized wake-shedding equation is reformulated into a continuous-time representation via first-order linear approximation, thereby deriving a continuous-time state-space panel method model incorporating viscous effects. Validation was conducted through unsteady aerodynamic simulations of a National Advisory Committee for Aeronautics (NACA0012) airfoil undergoing harmonic pitch oscillations. Results demonstrate that boundary layer viscous correction elevates the accuracy of the state-space panel method to levels comparable with computational fluid dynamics (CFD), while computational time remains below 0.5% of CFD-based approaches. To further showcase the method's versatility in aeroelastic applications, a two-degree-of-freedom pitch-plunge wing segment model was constructed. A softening cubic nonlinearity was introduced into the pitch degree of freedom, coupled with the state-space panel method to form a continuous-time nonlinear aeroelastic model. Finally, comprehensive analyses were performed on the model's static aeroelastic deformation, dynamic response trajectories, and flutter stability boundaries.