A semi-analytical method for nonlocal buckling and vibration of a single-layered graphene sheet nanomechanical resonator subjected to initial in-plane loads

A semi-analytical method named Galerkin strip distributed transfer function method (GSDTFM) is employed to solve the buckling and vibration of a single-layered graphene sheet (SLGS) nanomechanical resonator subjected to initial in-plane loads within the framework of the nonlocal Kirchhoff plate theory. The buckling load and the frequency shift are obtained by using the GSDTFM. And the effects of the initial in-plane load, the nonlocal parameter as well as the attached nanoparticle location on the frequency shift are investigated. The simulated results show that the buckling load of the SLGS depends on not only the side length of the SLGS, but also the small scale effects. The impact of the initial in-plane load on the fundamental frequency is significant. The frequency shift at an initial tensile load is larger than that at an initial compressive load. These results are consistent with the previously reported ones.