Application of SSPH Method in Free Vibration Analysis of Graphene

In this paper, the symmetric smoothed particle hydrodynamics (SSPH) as a meshless method is explained in detail. Free vibration analysis of bilayer graphenes with interlayer shear effect is modeled. The bilayer graphene is modeled as a sandwich beam with free-clamp end condition. To obtain the governing equations, each graphene layer is modeled based on the Euler-Bernoulli theory and in-plane displacements are also considered in addition to the transverse displacement. It is also assumed that the graphene layers do not have relative displacement during vibration. The results obtained by the sandwich beam model solved by SSPH method, include the first two natural frequencies of the bilayer graphenes. These results are validated by the molecular dynamic and compared with the GDQM results reported in the literature.