Surface- and nonlocality-dependent vibrational behavior of graphene using atomistic-modal analysis

•Developing a hybrid atomistic-continuum model for vibrational analysis of graphene.•The asymmetric and axisymmetric vibrational modes are studied.•The circular graphene sheet demonstrates a softening behavior.•Estimation of the surface parameters using comparison of MD and continuum models.•Non-local surface elasticity model has the best precision. Classical continuum theories are incapable of accurately describing the behavior of nanostructures due to their size dependence. Size-dependent effects such as surface and non-local are among these phenomena, and their study at the nano-scale is essential. Despite advances in modeling and characterization of graphene's material properties, the surface and nonlocality effects of circular graphene nano-plates have not been calibrated for continuum mechanics theories. Based on a hybrid model that combines the advantages of continuum and atomic models, the present study is primarily focused on developing a method for calculating and estimating the effect of these parameters. A non-local surface elasticity model for graphene has been developed using a modal analysis derived from molecular dynamics simulations based on genetic algorithm optimization. In this research, both asymmetric and axisymmetric linear vibrational modes are studied. The parameters of the model, including surface residual stress, surface elasticity, surface density, and size parameter, are extracted from the results of the atomistic modal. Subsequently, this hybrid atomistic-continuum model has been employed to characterize the vibrational behavior of graphene. Based on the conducted simulations, the surface elasticity model with the nonlocality effect is calibrated with the lowest error for all radii and vibration modes. Moreover, this research suggests using a non-local surface elasticity model for very small radii since its findings are remarkably similar to the molecular dynamics simulations for the same diameters. On the other hand, the error is highest for the continuum model that does not incorporate surface and non-local effects. The findings of this study can be valuable in evaluating the crucial parameters regarding the surface and non-local elasticity of two-dimensional structures. [Display omitted]