Multiscale nonlinear dynamics analysis of defective graphene reinforced PMMA composite plates under aerodynamic pressure

Structural defects in graphene are inevitable during the production process, which have remarkable impacts on the mechanical properties of graphene and further affect the properties of nanocomposite reinforced by graphene. In this work, a bottom-up multiscale approach is employed to investigate the nonlinear dynamics of defective graphene reinforced composite plates from the material properties of nanocomposites to the dynamic behavior of macro-composite plates. The molecular modeling and simulation are conducted by molecular dynamics (MD) to evaluate the effective mechanical properties of pristine graphene, vacancy defective graphene, Stone–Wales defective graphene, poly (methyl methacrylate) (PMMA) and graphene/PMMA composites reinforced by different graphene configurations at the nano-scale. Meanwhile, the fracture mechanism and interfacial interaction energy between graphene and PMMA matrix during the deformation process are examined to explore the enhancement mechanism of nanocomposites. The efficiency parameters are derived by incorporating the MD results and the extended Halpin–Tsai micromechanics model to capture the heterogeneity of nanocomposite at the nano-scale as well as the continuum scale, and then the effective material properties considering the effect of defect, temperature and pressure are substituted into the nonlinear dynamics of functionally graded graphene reinforced composite (FG-GRC) plates at the macro-scale. The governing equations of motion for FG-GRC plates under the aerodynamic pressure are derived based on the third-order shear deformation theory, von-Karman nonlinear strain–displacement relation and Hamilton’s principle. The aerodynamic pressure acting on the surface of the plate consists of two parts, one is the static pressure, and the other is the disturbed air flow. Furthermore, Galerkin method and the fourth-order Runge–Kutta method are exploited to discrete and solve the governing equations of motion. The bifurcation, time history and phase diagrams of FG-GRC plates are obtained to analyze the dynamic characteristics of the plates. This study reveals the nonlinear dynamic characteristics of graphene/PMMA composite plate, which contributes to the prediction of dynamic response of composite structure in the aerospace field.