## 1 Introduction  
Due to the recent advancements in science and technology [1; 2; 3; 4; 5; 6; 7; 8; 9], graphene nanoplatelet (GPL) reinforcement has attracted considerable attention. Some applications of GPL reinforcement are reported in Ref. [10]. Also, the mechanical properties of GPL reinforcements make them an appropriate choice to be used in chemistry, physics, electrical engineering, materials science, and nanoengineering applications [10]. [PERSON] et al. [11] compared the fracture characteristics of the functionally graded (FG) cemented carbide reinforced by the GPL with pure ones. They showed that the property of GPLs stops nanocracks in the nanocomposites. Furthermore, an experimental study by [PERSON] et al. [12] showed that the mechanical properties of epoxy nanocomposites are reinforced by different reinforcements such as GPL, multiwalled carbon nanotube (MWCNT), and single-walled carbon nanotube (SWCNT). Their work showed that the reinforcement GPL makes structures stronger and stiffer than other reinforcing. Furthermore, many studies express that adding a small amount of GPL causes a considerable change to the thermo-electro-mechanical aspects of the properties of the systems. In the past several years, it was remarkable that the micro and nano parts strengthened by GPLs are much more practical in industrial fields, and for this reason, the dynamic features of the nanostructures reinforced with GPL is a vital field of analysis. Based on nonlocal strain gradient theory (NSGT) and by considering the thermal effects, [PERSON] et al. [13] investigated the small-scale influences on a size-dependent laminated composite cylindrical nanoshell. They showed that the ply angle is more vital in the phase of the velocity of nanostructures and the higher wavenumbers. The wave propagation in the laminated cylindrical microshell was scrutinized basis on NSGT and strain gradient theory by [PERSON] et al. [14] Their results indicate that the phase velocity has an increment by decreasing the nonlocal constant parameter. Based on NSGT in the context of a high-order shear deformation beam theory, [PERSON] et al. are studied the frequency behavior of a postbuckled GPLs-reinforced composite (GPLRC) micro/nano beam [15]. Their results demonstrate that in the prebuckled region, the fundamental frequency of the system decreases by increasing the value of the nonlocal parameter. Furthermore, numerous researches [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39] scrutinized the stability and instability regions of the complex micro- and nano-structures by utilizing numerical and analytical procedures. In the field of critical temperature study of micro- and nano-structures, by considering the thermal effects of the environment and the axial force, the size-dependent postbuckling and buckling characteristics of cylindrical nano panels are analyzed by [PERSON] et al. [40]. They found that the value of the minimum load of the post-buckling domain cannot be affected by the thermal influences of the environment. [PERSON] and [PERSON] [41] investigated the nonlocal electro-thermomechanical instability of an FGM nano panel based on a new shear deformation theory, which contains exponential shear stress distribution. The nano panel has been covered by piezoelectric sheets, and the temperature effects have been considered. They displayed that by considering the nonlocality size effects, the related minimum load of the postbuckling domain increases, while the critical buckling load decreases. [PERSON] et al. [42] scrutinized the nonlinear instability analysis of an electrical nanoshell based upon NSGT. It can be demonstrated from their results that the strain gradient size dependency leads to increases the buckling stiffness, while the nonlocal size effect cause to decreases it. [PERSON] et al. investigated the size-dependent FG doubly curved panel [43]. They applied first-order shear deformation theory and the modified couple stress.