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In this research, natural frequency response of functionally-graded multilayer graphene-reinforced composite plate with circular cutout reinforced by orthogonal stiffeners is investigated for the first time. The structure is surrounded by Winkler-type elastic support. The plate is composed of polymethyl methacrylate (PMMA) as matrix material and reinforced by graphene platelets (GPLs). The material of the orthogonal stiffeners is the same as that for the matrix. Rule of mixtures and Halpin–Tsai approach are applied to estimate the effective material properties of the composite plate. Third-order shear deformation plate theory and finite element procedure is employed to obtain the element matrices of the structure. Natural frequencies and mode shapes of the stiffened plate are reported for different variables such as nanofillers dispersion patterns, width and height of the stiffeners, aspect ratio of plate, plate thickness ratio, weight fraction of nanofillers, number of stiffeners, boundary conditions, elastic foundation stiffness parameter and size of circular cutout. The obtained results denote that with the addition of a set of stiffeners, fundamental frequency enhanced up to 32.3% with just about 10% increase of mass. [ABSTRACT FROM AUTHOR]