▎ 摘　　要

A size-dependent improved third order shear deformable computational framework with the aid of modified couple stress theory (MCST) is developed to investigate the stability and free vibrations of polymer-based microbeams reinforced by graphene oxides (GOs). The nanocomposite microbeams are placed in an elastic substrate and have different immovable end restraints. The modulus of elasticity of the GOs-reinforced nanocomposite (GORC) is evaluated using the well-known Halpin-Tsai micromechanics model, and the equivalent mass density as well as Poisson's ratio is evaluated based on mixture rule. The equations governing the stability and vibration behaviors are derived by means of the Lagrange method with the help of the Gram-Schmidt process that is used to produce admissible functions in a general orthogonal polynomial form. The static stability and vibration characteristics of the GORC microbeams are analyzed. The influences of small-scale effect, GO nanofillers, and elastic foundation on the mechanical stability and vibration behaviors of the nanocomposite microbeams are illustrated using some numerical examples.