Plate-Beam Coupling Dynamic Modeling and Aeroelastic Analysis of Morphing Trailing Edge Flexible Wings

Under aerodynamic loading, morphing wings designed with compliant and lightweight principles are susceptible to structural responses that may lead to aeroelastic instability. The morphing trailing edge wing with chordwise non-uniform stiffness characteristic no longer satisfies the rigid section assumption of beam theory, making traditional beam models unsuitable, particularly for high aspect ratio wings. In this study, the Rayleigh-Ritz method is used to model the rigid front and flexible trailing sections of the morphing trailing edge wing as Euler beams and Kirchhoff plates, respectively. By considering the bending and twisting of the rigid front edge and the out-of-plane motion of the flexible trailing edge, a coupled plate-beam coupling dynamic equation is derived. Comparison with experimental results and finite element models shows that the analytical model accurately predicts the structural responses, including bending, twisting, and out-of-plane motion. Using unsteady aerodynamic theory for two-dimensional rigid-flexible coupled wings and strip theory, a high-accuracy low-order aeroelastic model is developed in modal space. Comparisons with cantilever plate flutter test results and Nastran aeroelastic numerical models confirm the model's accuracy in predicting flutter speed and frequency. Further analysis of key structural parameters reveals that as the flexibility ratio increases, the flutter speed decreases. When the flexibility ratio is small, the morphing trailing-edge wing exhibits a higher flutter speed compared to a constant cross-section cantilever wing.