To reduce the storage and transportation space， folding fin configurations are widely used in aircraft. For dynamic systems of folding fin with nonlinear connections， the fin is modeled based on the Mindlin plate theory， and unsteady aerodynamic is simulated by third-order piston theory. The Newmark method and Newton method are used to solve time domain displacement response of the fin with non-linear boundaries. The aeroelastic stability and displacement response of the folding fin of the aircraft are analyzed using the frequency domain and time domain methods. The influence of nonlinear types and parameters of folding mechanisms on aeroelastic behavior is discussed. The results show that the difference of natural frequency and unsteady response results of the established model， and that from the commercial finite element results is less than 2.2%， indicating a good consistency and verifying the correctness of the structural dynamics model. For polynomial nonlinear connection stiffness， it exhibits a convergence trend under critical velocity conditions； for freeplay nonlinearity and bilinear connection stiffness， there is a gradual divergence trend under critical speed conditions. At a 0.5° freeplay condition， the vibration amplitude of bilinear stiffness is significantly smaller than that of freeplay stiffness， indicating that pre-installing torsion springs in freeplay folding mechanisms can significantly reduce vibration response； for asymmetric mixed nonlinear stiffness， this model exhibits a gradually divergent trend under critical velocity conditions. This method has certain guiding significance for the research of fluid structure coupling problems in aircraft and the evaluation of vibration response of folding fin with nonlinear connections under flight conditions.