Analysis of flutter characteristics of supersonic carbon nanotube-reinforced beams

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.