Dynamic analysis of single-layer graphene sheets

In this paper, an equivalent dynamic model of single-layer graphene sheets (SLGSs) is developed by using molecular mechanics (MMs) based finite element (FE) approach where bond interactions are represented by beams; then, two- and three-dimensional modal and transient analyses of SLGSs are completed. In order to observe vibrational characteristics of SLGSs, lumped mass matrix is generally used in literature, which is sufficient to determine vibrational characteristics of graphene sheets (GSs) and carbon nanotubes (CNTs). As mass lumping by neglecting rotational inertia of beam elements causes singularity problems in transient analysis, consistent mass matrix is used in FE models in this study. An equivalent density parameter for the beam elements is derived by using the equivalency of natural frequencies of the MM model and continuum plane-stress FE model. The Newmark method is employed to integrate the associated equations of transient analyses. It is shown that the proposed approach can reflect two- and three-dimensional vibrational characteristics of SLGS similar to the lumped mass and plane stress models. In addition, the power spectral density properties of transient analyses are in good agreement with modal features of SLGSs.