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This is the first research on the frequency analysis of a graphene nanoplatelet composite circular microplate in the framework of a numerical-based generalized differential quadrature method. Stresses and strains are obtained using the higher order shear deformation theory. The microstructure is surrounded by a viscoelastic foundation. Rule of the mixture is used to obtain varying mass density and Poisson’s ratio, whereas the module of elasticity is computed by a modified Halpin–Tsai model. Governing equations and boundary conditions of the graphene nanoplatelet composite circular microplate are obtained by implementing Hamilton’s principle. The results show that outer to inner radius ratio [Formula: see text], ratios of length scale and nonlocal to thickness ( l/ h and [Formula: see text]), and graphene nanoplatelet weight fraction [Formula: see text] have significant influence on the frequency characteristics of the graphene nanoplatelet composite circular microplate. Another necessary consequence is that by increasing the value of [Formula: see text], the distribution of the displacement field extends from radial to tangent direction, especially in the lower mode numbers; this phenomenon appears much more remarkable. A useful suggestion of this research is that for designing the graphene nanoplatelet composite circular microplate at a low value of [Formula: see text], [Formula: see text] and [Formula: see text] should be given more attention, simultaneously. An interesting result which has come down from the article is that the effect of [Formula: see text] on the dimensionless frequency of the structure is really dependent on the value of C d.

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