▎ 摘　　要

Two-dimensional nanomaterials exhibit specific mechanical characteristics essential for commercialization and industrial applications, such as nano electro-mechanical systems. When analyzing a mechanical field, it is important to determine these materials' bend-ing stiffness and stretching properties. The apparent bending stiffness and stretching of graphene structures at the macro-scale differ from theoretical predictions at the nano -scale. This discrepancy results from thermally generated dynamic waves in these atomic -based structures. Therefore, characterization methods based on atomistic static methods were unable to capture these effects. This study uses hybrid atomistic-continuum models to apply modal analysis to determine these key parameters. The proposed approach ex-ploits the advantages of both atomistic and continuum models. Our approach is based on optimization techniques such as the simulated annealing algorithm. The unknown parame-ters of the continuum models, such as the bending stiffness and stretching, were acquired from molecular dynamics simulations and continuum mechanics resonance frequencies. The effects of diameter on the mechanical properties and value of different mode shapes of graphene nanostructures are studied using this method, which incorporates the effects of nano and macro-scale models. The presented approach provides insight into the me-chanical vibrational characteristics of two-dimensional graphene structures at an atomic level. (c) 2022 Elsevier Inc. All rights reserved.