On the theoretical and molecular dynamic methods for natural frequencies of multilayer graphene nanosheets incorporating nonlocality and interlayer shear effects

Abstract

In this paper, a multiplate nonlocal shear model and molecular dynamic simulations are presented to investigate the effects of interlayer shear and nonlocality on the natural frequencies of multilayer graphene sheets (MLGSs). From one aspect in the optimal design of such structures, the interaction between graphene layers, which can significantly vary the static and dynamic behavior due to lack of solidity of layers stack, should be considered. On the other hand, it is requied that the nonlocality phenomenon which has an effective role in the mechanical analysis of nanostructures is taken into account. To this aim, the equation of motion along with corresponding boundary conditions is derived by using the Kirchhoff plate model and nonlocal continuum theory to capture these effects. For a case study, the free vibration problem of simply supported MLGSs is studied by presenting the closed-form Navier’s solution of natural frequencies and carrying out Molecular dynamics (MD) simulations to estimate the value of nonlocal parameter. Finally, the influences of interlayer shear modulus, number of layers, foundation stiffness, and nonlocal parameter on the natural frequencies of such MLGSs are examined in detail. Findings show that natural frequencies including nonlocality effect become smaller than ones of the classical continuum theory and also have good agreements with MD simulations. Moreover, it is seen that the sensitivity of natural frequency to the nonlocal parameter becomes more significant when the number of layers or interlayer shear modulus increases as well as the aspect ratio or width of sheets decreases.