small scale effect on vibration of thermally postbuckled monolayer graphene nanoribbon based on nonlocal elasticity theory

In the present research, vibration behavior is presented for a thermally postbuckled two side clamped monolayer graphene nanoribbon. the monolayer graphene nanoribbon is modeled as      a nonlocal orthotropic plate strip which contains small scale effects. the formulations are based on   the kirchhoff’s plate theory, and von karmantype nonlinearity is considered in straindisplacement relations. the thermal effects are also included and the material properties are assumed to be temperaturedependent. the initial deflection caused by thermal postbuckling and internal loads are taken into account. a coupled system of equations is derived and a new semi analytical solution is obtained. the effects of variation of small scale parameter e0 a to the natural frequencies, deflections and mode shapes of graphene nanoribbon are analyzed and the numerical results are obtained from the nonlocal plate model; also, molecular dynamics simulations are used to investigate different properties of graphene nanoribbon including both buckling and vibrational behaviors. the small scale coefficient is calibrated using molecular dynamics simulations. numerical results are compared with those of similar researches. effects of various parameters on the postbuckled vibration of graphene nanoribbon in thermal environments such as scale parameter, length and thermal load are presented. stability and occurrence probability of internal resonance between vibration modes around a buckled configuration is investigated.