Influences of the graphene reinforcements on the natural vibrational properties, nonlinear flutter responses, and the chaotic motions of the FG-GR laminated composite cantilever rectangular variable cross-section plate in the supersonic flow

Abstract

Due to the excellent mechanical and lightweight properties of the graphene-reinforced composite structure, it can meet the design requirements of modern aircraft comments. In this paper, the aircraft wings with low aspect ratio are modelled as the functionally graded graphene-reinforced laminated composite cantilever rectangular (FG-GRLCCR) variable cross-section plate. The influences of the graphene reinforcements on the natural vibrational properties, the nonlinear flutter responses, and the chaotic motions of the FG-GRLCCR variable cross-section plate are investigated. The extended Halpin-Tsai model is used to calculate the mechanical parameters for the graphene-reinforced composite materials. The first-order piston theory is applied to simulate the aerodynamic force on the FG-GRLCCR variable cross-section plate in supersonic flow. Considering the classical laminated theory, the von Karman large deformation theory, and the simple harmonic excitation, the dynamic partial differential equations for the FG-GRLCCR variable cross-section plate are derived by the Hamilton principle. The nonlinear ordinary partial equations of the system are given based on the Galerkin truncation technique. The frequency loci veering phenomenon and vibrational mode interaction for the FG-GRLCCR variable cross-section plate are obtained by the Rayleigh-Ritz method. The nonlinear flutter responses of the FG-GRLCCR variable cross-section plate are analyzed before and after critical flutter pressure. The bifurcation diagrams, Maximum Lyapunov exponent diagram, phase diagram, waveform diagram, and Poincaré cross-section diagram of the system are depicted for investigating the influence the graphene reinforcements on the nonlinear dynamic responses. The results showed that the graphene reinforcements and distributed patterns can change the frequency loci veering phenomenon, improve the critical flutter pressure and reduce the occurrence of chaotic motions of the FG-GRLCCR variable cross-section plate.