On the hybrid atomistic-continuum model for vibrational analysis of α-, β-, and γ-graphyne circular nano-plates

Abstract

The natural frequency of graphyne structures for all phases is calculated by molecular dynamics simulation. Tersoff potential function was used in molecular dynamics (MD) simulations. In this paper, the vibration behavior of α-, β-, and γ-graphyne circular nano-plates was investigated using a hybrid atomistic-continuum Model. The MD frequencies are higher than those obtained from the classical local plate model, so the use of the Eringen-nonlocal elasticity model is practically unusable. The obtained equations based on the stress-driven elasticity, modified couple stress theory, and strain gradient theory were solved by generalized differential quadrature rule (GDQR), which has a faster convergence than generalized differential quadrature method (GDQ). The value of the size parameter for each diameter was calculated using the molecular dynamics results. By changing the phase from alpha to beta and beta to gamma, value of stiffness is increased. Therefore, for a smaller size parameter, continuum mechanics results match the molecular dynamics results. The results show that the size effect parameter is not a fixed value and has different values in different conditions. For all three phases and all diameters, the calculated frequencies are greater than those from classical theory. This result shows that the graphyne structure is fantastic and peculiar.