Free vibration analysis for single-layered graphene sheets in an elastic matrix via modified couple stress theory

Free vibration of single-layered graphene sheet (SLGS) resting on an elastic matrix as Pasternak foundation model is investigated by using the modified couple stress theory. Governing equation of motion for SLGS is obtained via thin plate theory in conjunction with Hamilton’s principle. All edges simply supported boundary condition is considered. Analytical solution of the resulting equation is obtained via Fourier series approach. Effects of the material length scale parameter and elastic matrix parameters on vibration frequencies of SLGS are investigated. The influence of the mode numbers on frequencies for two-different matrix parameters and aspect ratio of graphene sheet are also studied. Numerical results reveal that the frequency values increase significantly with the increase of the material length scale parameter. It has been shown that scale effects are quite significant on frequencies especially when length and width of the SLGS is smaller and in higher modes of vibration and need to be included in the mechanical modeling of SLGS.