## 1 Introduction  
The continuous development of novel materials with increased mechanical performances and low density has encouraged the adoption of novel reinforcements, such as carbon nanotubes and graphene platelets. It is well known from the literature that the addition of carbon nanotubes and graphene platelets within a matrix leads to a general increase of the structural stiffness and a decrease of the density. In the experimental results by [PERSON] et al. [1], for example, the Young's modulus of the epoxy matrix was increased by 31%, with the addition of 0.1% of graphene platelet reinforcement. Based on another experimental investigation performed by [PERSON] et al. [2], the introduction of 0.7% of weight fraction of graphene platelet reinforcement in the matrix was demonstrated to increase the tensile strength by 76%, and the Young's modulus by 62%. Despite a large amount of experimental and theoretical studies, the literature has focused on the mechanical response of structures reinforced with carbon nanotubes, with an increased attention has been paid to composite structures reinforced with graphene nanoplatelets (GPLs), as in the following review. [PERSON] et al. [3] analytically studied the vibration behavior of functionally graded (FG) graphene-reinforced composite laminated plates, accounting for the nonlinear strain field and the presence of an elastic foundation. A perturbation method was adopted by the authors to derive the nonlinear natural frequencies of FG graphene-reinforced composites, and to evaluate the sensitivity of the mechanical response to different boundary conditions, reinforcement patterns, and foundation parameters. A buckling analysis of cylindrical shells reinforced with graphene platelet was also performed by [PERSON] et al. [4], where the effective mechanical properties of the material were evaluated based on the Halpin-Tsai micromechanical model and the rule of mixtures. The free and forced vibration response of FG multilayer GPL/polymer composite plates was also studied by [PERSON] et al. [5], according to the first-order shear deformation plate theory. [PERSON]'s solution was proposed to derive the explicit expressions for natural frequencies and amplitudes of free and forced vibrations. Based on a parametric investigation, the authors verified the high sensitivity of the mechanical response on the GPL weight fraction, as well as on the number of layers and dimensionless geometrical parameters. In addition, [PERSON] et al. [6] presented the main results of a nonlinear free vibration analysis of beams reinforced by graphene platelets. The problem was formulated according to the [PERSON]'s beam theory and solved numerically by applying the Ritz method. The authors, in their work, verified the high sensitivity of the nonlinear vibration response to different reinforcement distributions, weight fractions, geometry, dimensions, and total number of layers. A different approach based on the third-order shear deformation theory and nonlocal strain gradient beam model was used by [PERSON] and [PERSON] [7] for the nonlinear vibration analysis of FG graphene platelet-reinforced composite nanobeams. [PERSON]'s principle was used to derive the nonlinear governing equations of motion, whereas an analytical expression for the nonlinear size-dependent natural frequencies was determined by means of the perturbation technique and [PERSON] method. [PERSON] et al. [8] investigated the bending and vibration response of FG trapezoidal plates reinforced with GPLs based on the finite element method. In detail, the effective modulus of elasticity, together with the Poisson's ratio and density, were computed according to the Halpin-Tsai micro-mechanical model and the rule of mixtures. The static and dynamic behavior of the reinforced plate was evaluated for varying patterns and weight fractions of GPL. A further work based on [PERSON]'s beam theory and von Karman nonlinear relations was proposed by [PERSON] et al.