Today, vibration analysis has proven to be one of the most important tools in the maintenance of mechanical and electronic equipment. Vibration and frequency analysis can be used to predict the behavior of materials used in mechanical and electronic devices. Graphene sheets are also widely used in the manufacture of nano- sensors and resonators, so it is important to study the frequency and vibration behavior of nano-graphene sheets. In this research, an attempt is made to use the scaled boundary finite element method to analyze the frequency and vibration of the graphene sheets. This method is one of the newest numerical methods that has been considered in recent years due to its special features. The scaled boundary finite element method has the advantages of both the boundary finite element and finite element methods but is currently less commonly used at the nanoscale. In this research, for the first time, this method at the nanoscale has been used to analyze the frequency and vibration of nano-graphene plates. For this purpose, hexagonal elements corresponding to the honeycomb structure of graphene were used. Equivalent energy criteria were also used in the simulation. In this study, the results of vibrational and frequency analysis were presented using the scaled finite element method, in different boundary conditions for single-layer graphene and different molecular orientations at in-plane degrees of freedom. The transient response of the graphene sheet to the harmonic concentric load was also studied. The results are in good agreement with the results of molecular dynamics and finite element methods and show that the natural frequencies of the system decrease with increasing model dimensions. It was also observed that the orientation of the molecules in the two directions of the armchair handle and the zigzag does not have much effect on the natural frequencies of the system. Vibration analysis was also applied to the graphene nanoribbons under concentrated load for cantilevered and bridged boundary conditions at the applied harmonic load with frequencies of 10 and 100 GHz, which showed more displacement in the cantilevered state than in the bridged state. Also, regarding the orientation of the molecules in the two directions of the armchair handle and the zigzag, a significant increase in the maximum displacement in the zigzag mode can be observed compared to the direction of the armchair handle at a frequency of 100 GHz. Keywords Nano Graphen, Energy equivalent model, Scaled bouandary Finite Element Method, Frequency Analysis, Vibration Analysis