Rigid–Elastic Coupling Aeroelastic Modeling for Flexible Aircraft: From a Gibbs Function Perspective

As the structures of flying-wing aircraft become increasingly flexible, body freedom flutter (BFF) poses a significant threat to flight safety. This study presents a novel and general methodology for deriving the rigid–elastic coupling equations of motion for flexible aircraft, enabling accurate predictions of BFF. Unlike conventional approaches based on momentum or energy formulations, this method is developed from the perspective of the Gibbs function, which provides a unified representation of the system’s dynamic states. Within the Appell dynamics framework, the incorporation of the Gibbs function facilitates the natural and effective treatment of non-holonomic constraints, particularly those arising from Euler’s rotational equations during maneuvering flight. This framework for flexible aircraft is compact and well-suited for modeling rigid–elastic coupling dynamics within a unified framework. The proposed method is applied to analyze the BFF boundary of a flexible flying-wing aircraft. The relative error between the theoretically predicted BFF boundary and the flight test results is less than 6%. Numerical results demonstrate that the modeling method effectively predicts the BFF boundary. Furthermore, the effects of maneuvers on the rigid–elastic coupling system at different load factors are also investigated using the modeling method.