مريم رحمتي صالح كوهي

Today, with the advancement of science and human access to nanotechnology and Application of this knowledge in various fields such as medicine, chemical, mechanical, electronic cause to the analysis of the behavior of nanoscale structures of great importance. In this study, graphene nanoparticles are examined in two environmental conditions of fluid and air despite surface imperfections. The governing equations for vibrations of nanoplate of graphene submerged in fluid are obtained from Erlingen's non-local elasticity theory.when nano plate of graphene submerged in fluid we can obtain the equation for the interaction between the fluid and the graphene by , using the Laplace equation and the fluid velocity potential. As a result, we calculate the difference in pressure from fluid on nano plate and putting in main equation to obtain Equations governing the vibration of graphene .in this paper vibrations are evaluated in two horizontal and vertical states. For the case where the nano-plate is vertical, the natural frequency is calculated for various sub-heights. Further, the natural frequency of the nanoplate of graphene with presence of cracks in the surface was investigated and the crack of nanoplate was simulation by Lattice Spring method (LSM) . Finally, differential equation method (DQM) was used to solve the governing equations of vibration of nanoplate. The effects of different parameters on the natural frequencies of graphene for different support conditions were investigated. The results of the study in six different boundary conditions it is significant that by increase of the parameter of non-local the natural frequency was decreased. Also, the presence of cracks decreased the natural frequency in all the different boundary conditions an‎d with the increase in the length and depth of the cracks, the natural frequency was decreased. At the end of the study, the variation charts of the various parameters are given with respect to the natural frequency.