In this research, a multi-scale model was used to analyze the vibrational behavior of the atomic force microscope (AFM) on a graphene sheet sample. Cantilever and silicone tip base were simulated based on the continuum mechanics using finite element modeling and the tip apex were modeled based on the Tersoff potential by the structural mechanics modeling. The contact behavior between the tip and graphene was investigated using measuring friction force during the tip movement on the graphene layer, and its results were compared to the results obtained from molecular dynamics simulation and experimental test. The friction force between the tip and graphene increases by enhancing the tip radius and the contact surface between the tip and the sample. Moreover, the friction force dwindles by heightening the number of graphene layers as a result of sliding graphene layers on each other and diminishing the Poker effect (wrinkling). With the initial distance displacement of the tip from the sample, two curves of the tip vibration amplitude variations and the phase change between tip vibration and excitation vibration were plotted, and the effect of crack and its location in the cantilever was studied. The results showed that the crack in the cantilever can dramatically influence the tip vibration amplitude and the phase change between the tip vibration and the excitation signal. تفاصيل المقالة