Based on the Von-Kármán deformation theory and the aerodynamic piston theory, the flutter model of functionally graded carbon nanotube reinforced composite(FG-CNTRC)beams was established. The governing equation of FG-CNTRC beams was derived by Hamiltonian principle, and the governing equation was discretized by using the Galerkin method, and the nonlinear differential equation was transformed into a nonlinear differential equation. The Hurwitz determinant was used to solve the nonlinear equation, and the root was used as the determination of Hopf bifurcation. Considering three different carbon nanotube distribution modes, the stability analysis of the FG-CNTRC beams with different parameters was carried out, the hydrostatic and aeroelastic deformation curves of the FG-CNTRC beam with different parameters were obtained. The influence of the aspect ratio of the beam on the dimensionless critical flow velocity and dimensionless critical dynamic pressure was analyzed, and the time history diagram, phase diagram and Poincare map under different parameters were verified by numerical calculation.

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.

To investigate the nonlinear static and dynamic characteristics of functionally graded graphene platelets reinforced composite beam(FG-GPLRC)under the combined action of aerodynamic load and temperature. A nonlinear vibration model of functionally graded graphene platelets(GPL) reinforced beam in supersonic flow is established based on the classical beam theory and first-order piston theory. Firstly, considering that GPL presents three different gradient distributions(U-GPLRC, OGPLRC and X-GPLRC)along the thickness direction, deriving the functional gradient graphene platelets reinforced beam aeroelastic control differential equation by applying Hamilton's principle. Secondly, using the Galliukin method, it is transformed into a nonlinear ordinary differential equation, and then the determination of the Hopf bifurcation is transformed into the root of the nonlinear equation using the stability criterion of the Routh-Hurwitz system. The effects of temperature, GPL mass fraction and distribution pattern on the stability of FG-GPLRC beam aeroelasticity were analyzed by parametric study. The solution yields dimensionless critical flow velocity, dimensionless critical frequency, and dimensionless dynamic pressure. Finally, the aeroelastic stability of the FG-GPLRC beam was verified by numerical calculations. the results show that the higher the mass fraction of gpl, the more significant the enhancement effect, and the x-gplrc distribution pattern has the best enhancement effect. the research results will provide theoretical reference for the design optimization of fg-gplrc beam.