Influences of Small-Scale Effect and Boundary Conditions on the Free Vibration of Nano-Plates: A Molecular Dynamics Simulation

This paper addresses the influence of boundary conditions and small-scale effect on the free vibration of nano-plates using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is used to obtain fundamental frequencies of single layered graphene sheets (SLGSs) which modeled in this paper as the most common nano-plates. On the other hand, governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different side lengths, boundary conditions, and nonlocal parameter are inspected for the aforementioned methods. The results obtained from the MD simulations are compared with those of nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. As a result, for the first time, the nonlocal parameter values are suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies.