Nonlinear vibration and postbuckling analysis of a single layer graphene sheet embedded in a polymer matrix

Nonlinear vibration and postbuckling behavior of a single layer graphene sheet (SLGS) embedded in a polymer matrix aroused by the nonlinear van der Waals (vdW) forces are investigated using the Kirchhoff plate theory. The interfacial vdW forces are described by a nonlinear function in terms of the graphene deflection. Through harmonic balance method, the nonlinear relation between deflection amplitudes and resonant frequencies of free vibrations of the SLGS and its postbuckling equilibrium path are derived. It is found that variation of resonant frequencies of an embedded SLGS is less dependent on the graphene aspect ratio and mode numbers as compared with a free-standing one. In-plane load effects upon the vibrational behavior of the SLGS and its postbuckling are also discussed. Simulation results have demonstrated the significance of considering the surrounding medium effect and its nonlinearity in the study of the vibration and buckling of the embedded graphene with applications in nanocomposties.