▎ 摘　　要

Recently, nano-reinforcements have been extensively implemented to enhance performance related to the structures due to overcoming the complex conditions faced in various facilities, such as aerospace components. For this reason, one of the novel nano-reinforcement named Graphene Oxide Powders (GOPs), counted as graphene-derived nano-reinforcements, is implemented here to upgrade vibrational performances related to structures. Based on this, 11 multipurpose structures, comprising Semispherical (SS), Spherical (S), Semielliptical (SM), Elliptical (E), Hyperboloidal (H), Paraboloidal (P), Conical (CO), and Cylindrical (CY) shells and Annular plate (AP) reinforced by GOPs are vibrationally investigated here. Accordingly, the Halpin-Tsai Homogenization Approach (HTHA) and the rule of the mixture are employed to characterize the GOP's mechanical factors. In addition, the General Shell Scheme (GSS) and the First Shear Deformation Theory (FSDT) are applied to discover the fundamental relationships associated with the structures. Next, Hamilton's principle determines the Differ-ential Motion Equations (DMEs) corresponding to structures. Followingly, the well-characterized mesh reduction procedure titled the Generalized Differential Quadrature Method (GDQM) is implemented to discretize the structures' DMEs. Subsequently, the Natural Frequencies Indicators (NFIs) are mined by managing the eigen-values evaluation. Because this examination involves an investigation related to multiple structures and can count as a comprehensive study and benchmark solution for future works, FEM-based simulation (only for validation study) is used to validate and confirm the present framework. In the end, multiple examples are designed and calculated to indicate the effects of the mass fractions and distribution patterns related to the GOPs on the NFIs related to the mentioned multipurpose structures.