Due to the efficiency of piezoelectric and piezoelectromagnetic materials in converting electro-mechanical and magnetic energies to each other, such materials arise in a wide range of fields and industries including heat exchangers, smart devices, nuclear devices and electromechanical systems [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12]. Moreover, such materials have a key role in nano-electro-mechanical systems such as sensors, actuators, nanogenerators, active controllers and nano-robotics [
13]. Generally, nanocomposite structures reinforced with graphene are the main component of these devices since they are well-known for their stunning electro-mechanical properties. As a consequence of this, a large number of academic works have been devoted to investigate the properties of such materials. Based on the theory of linear piezoelectromagneticity, Hu and Li [
8] obtained the expressions for singular stresses, electric displacements and magnetic fields in a piezoelectromagnetic plate with a Griffith crack subjected to longitudinal shear loads. Moreover, Ke and Wang [
14] determined the linear natural frequencies of size-dependent electromagnetic nanobeams under external electric, magnetic potentials and a uniform temperature field based upon the nonlocal-Timoshenko beam theory and nonlocal elasticity theory. In another piece of research, Ke et al. [
15] studied the free vibration behavior of magneto-electro-elastic (MEE) nanoplates employing the nonlocal and Kirchhoff plate theories. Employing the same mentioned nanobeams hypotheses, the bending, buckling and free vibration of MEE composites have been analyzed by Li et al. [
16], taking into consideration the small-scale-dependent coefficients and the strength of the electric and induced magnetic fields on the transverse displacement, rotation, buckling loads and natural frequency. Exact solutions for anisotropic functionally graded and multi-layer MEE rectangular plates with material properties varying exponentially along the thickness direction were proposed by Pan and Han [
17]. Farajpour et al. [
18] depicted a nonlocal plate model to consider the size-effect on the nonlinear vibration behavior of MEE composite nanoplates subjected to external electromagnetic loading conditions. Furthermore, Farajpour et al. [
19] considered the higher order deformations along with the higher and lower order nonlocal effects for the nonlinear bucking of orthotropic nanoplates in a thermal environment. Jamalpoor et al. [
20] determined the closed-form solutions for natural frequencies and mechancial buckling loads of double-MEE nanoplate systems exposed to initial external electric voltage and magnetic potentials embedded in a viscoelastic medium. Mehditabar et al. [
21] studied 3D magnetothermoelastic responses of FGM cylindrical shells using differential quadrature (DQ) technique subjected to non-uniform internal pressure. Under the influence of external electric voltage, Zenkour and Aljadani [
22] determined the electro-mechanical buckling behavior of simply supported rectangular functionally-graded piezoelectric (FGP) plates using a quasi-3D refined plate theory. The impacts of various parameters, such as magnetic parameters, electrical potentials, rotation speed, thickness-to-radios ratio, and axial and circumferential wave numbers, on the free vibration of the rotating FG polymer cylindrical shells integrated by two piezo-electromagnetic (PEM) face sheets were evaluated by Meskini and Ghasemi [
23]. Abazid and Sobhy [
24] explained the thermal and EM size-dependent bending of simply-supported FG piezoelectric (FGP) microplates embedded on a Pasternak elastic foundation depending on a novel refined four-variable shear deformation plate theory, with the help of modified couple-stress theory. Nanoplate problems subjected to hygrothermal loads have been proposed in [
25,
26], using different nonlocal theories. Chen et al. [
27] showed analytical formulations for the wave propagation studies in MEE multilayered plates with nonlocal properties, and selected two types of sandwich plates to investigate the nonlocal parameter on the dispersion curve. The impact of shear deformation and angular velocity on the wave propagation behaviours of MEE rotary nanobeams is performed by Ebrahimi and Dabbagh [
28], using the nonlocal strain gradient theory (NSGT). Furthermore, the thermomechanical buckling, free vibration and wave propagation in smart piezoelectromagnetic nanoplates in a hygrothermal medium embedded in an elastic substrate was explored by Abazid [
29]. In addition, some useful studies of sandwich structures in various configurations of FGPMs or FGPs, and subjected to various loadings, have also been performed by some eminent researchers [
2,
30,
31,
32].
Graphene reveals exceptionally superior electromechanical and physical properties (Potts et al. [
33]), and is composed of a single thick layer of sp
joined carbon atoms arranged in a 2D hexagonal form. Graphene is the most powerful material that has been detected, since its tensile strength equals about
GPa, it has a Young’s modulus greater than 1 TPa, a mass of 1 m
is
mg and electrical conductivity 1000 times greater than copper for electric current-carrying capacity (Papageorgiou et al. [
34]). Furthermore, the specific-surface-area of the graphene is exactly 2630 m
/g (Papageorgiou et al. [
34]), whereas that of carbon nanotubes is in the range of 100–1000 m
/g. Graphene has been investigated as an ideal effective reinforcement of the piezoelectric material composite structures due to it enhances their electromechanical features and stiffness (see, e.g., Yang et al. [
35], Forsat et al. [
36], Khorasani et al. [
11], Thai et al. [
37,
38] and Phung-Van et al. [
39]). Mao et al. [
40] presented the vibrational characteristics of the FG piezoelectric composite micro-plate reinforced with graphene nano-sheets (GNSs) upon the non-local constitutive relation and von-Karman geometric non-linearity, in which the equations of motion were solved via the differential quadrature (DQ) method. They showed that the concentration of graphene nano-platelets, exterior voltage, nonlocal parameters, geometrical and piezoelectric properties of the GNSs, as well as the elasticity parameters of the Winkler elastic foundation, has a key insight in the linear and nonlinear dynamic behaviors of the GNSs reinforcing FG piezoelectric composite micro-plates. Sobhy [
41] developed an analytical method for the ME-thermal bending of FG-GNSs reinforced composite doubly-curved shallow shells surrounded by two smart face sheets of PEM with several boundary conditions. The obtained results of Mao and Zhang [
42] showed that the piezoconductive characteristics of the GNSs nanofillers can significantly improve the stiffness of the FG-GNSs plates. Mao and Zhang [
43] investigated the post-buckling and buckling properties of FG-GNSs plates subjected to electric potential and mechanical loads, in which the equations of motion were obtained by the combination of differential quadrature method and direct iterative technique. Furthermore, Sobhy et al. [
44] investigated the change in thermal buckling in PFG-GNSs beams exposed to external electric voltage in a humid environment. In addition, some experimental works have shown that graphene reinforcements can obviously enhance the mechanical properties of the piezoelectric. Abolhasani et al. [
45] investigated the influence of graphene reinforced PVDF (polyvinylidene fluoride) composites on the morphology, crystallinity, polymorphism and electrical outputs, on which the enhanced PVDF/graphene can be a potential application for portable self-powering devices. Xu et al.’s experiments [
46] showed the positive piezoconductive impact in suspended graphene layers, which strongly depends on the layer-number.
As viewed in the above survey, many papers have been performed to study the behavior of GPL reinforced piezoelectric plates. However, the GPL reinforced piezoelectromagnetic (PEM) plate has not been considered in the literature. Motivated by this deficiency and to fill this gap, the present article is conducted to provide a comprehensive and clear scientific vision for the free vibration of piezoelectromagnetic plates reinforced with functionally graded graphene nanosheets (FG-GNSs) under simply supported conditions. In addition, a refined four-variable shear deformation theory is introduced to define the displacement field. The present nanocomposite panel is assumed to be resting on a Winkler–Pasternak foundation and subjected to external electric and magnetic potentials. The electric and magnetic properties of the GNSs are assumed to be proportional to those of the electromagnetic plate. Moreover, in accordance with the modified Halpin–Tsai model, the effective material properties of the plate are evaluated. To govern the variation in the volume fraction of graphene through the thickness of the plate, a refined graded rule is used. Hamilton’s principle is employed effectively to deduce equations of the motion mathematically, and then solved analytically to obtain the eigenfrequency. In order to validate the present formulations, the depicted results are compared with the published ones. Furthermore, the detailed parametric investigation of the variation in various parameters on the vibration of the smart plate are discussed.