Document Type : Original Article

**Authors**

Department of Mechanical Engineering, University of Shahrekord, Iran

**Abstract**

In this paper, the free vibration of defective nanographene is investigated using Molecular Dynamics Simulation (MD) and Differential Quadrature Method (DQM). The equations of motions and the related boundary conditions are derived based on the differential constitutive relations in conjunction with the classical plate theory via Hamilton’s principle. Then, DQM is used to investigate free vibration of the nanographene with various boundary conditions. At first, in order to determine natural frequencies more realistically, nanographene mechanical properties are determined using MD simulations. The effects of defects are investigated by analyzing pristine and defective nanographenes containing Stone Wales, vacancy, and Adatom defects. According to the results, the non-dimensional fundamental natural frequency parameter converges to the analytical value for N=10×10. Results indicate that graphene with CCCC boundary conditions has the maximum natural frequency. The minimum value corresponds to the graphene with SSSS boundary conditions. In addition, Non-dimensional fundamental frequency parameter of the nanoplate increases with increasing nanoplate aspect ratio. Finally, defects reduce density, position ratio and elastic moduli of nanographene, which causes a decrease in natural frequency. Stone Wales and vacancy defects decrease nanographene natural frequencies by about 8 and 25 percent, respectively.

**Keywords**

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