▎ 摘　　要

.Application of the Rayleigh-Ritz method for the vibration problem of a porous multi-scale hybrid nanocomposite graphene oxide powder (GOP)/carbon fiber (CF)-reinforced beam is shown here for the first time on the basis of a new refined higher-order shear deformation beam theory. The structure consists of an initial matrix which is strengthened via both macro- and nano-scale reinforcements. Herein, GOPs and CFs are selected to be dispersed inside the resin. Moreover, the influences of porosity are included, too. The governing equations of the problem are achieved in the framework of a new refined higher-order beam model. Afterward, the Rayleigh-Ritz well-known finite-element method (FEM) is implemented to solve the problem for various boundary conditions (BCs). The validity of the presented formulation is checked by comparing the results of the employed FEM with those achieved from the Navier solution. it is shown that hybrid nanocomposites are able to support higher natural frequencies in comparison with either conventional fiber-reinforced composites or common two-phase GOP-reinforced nanocomposites.