Nonlinear static and dynamic characteristics of functionally graded graphene platelets reinforced beam in supersonic flow

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.