Analysis of nonlinear flutter characteristics of S-shaped functionally graded composite beams

Based on the classical beam theory and the first-order piston aerodynamic theory, the nonlinear flutter characteristics of S-shaped functionally graded composite beams are investigated for the mechanical behaviors such as flutter that may occur during the supersonic flight of aircraft. Considering two types of S-shaped functionally graded materials (S-FGM) composite beam structures, the Galerkin method is used to discretize the system control equation, combining with Routh-Hurwitz stability criterion and Hopf bifurcation theory, the analytical expressions of the critical velocity and frequency are derived. The stability performance of the two types of composite beams is compared through an example, and the influence of key physical parameters such as temperature stress, gradient index and aerodynamic stiffness coefficient on the flutter stability of S-type functionally graded beams is systematically studied. Finally, the stability of the system is verified by Runge-Kutta method. The results show that with the increase of the functionally graded index, the system will be more prone to flutter. The research results will provide a theoretical basis for the design optimization of S-shaped functionally graded composite beams.