## 1 Introduction
Their results investigate various parameters such as aspect ratio, the influences of material length scale, and panel curvature. [PERSON] et al. [44] introduced an exact novel model based on surface elasticity and Kirchhoff theory to determine the vibration performance of a double-layered microstructure. The surface effect is captured in their model as the main novelty. The results obtained with the aid of their modified model showed that the vibration performance of the double-layered microstructure is quite higher than the single-layered one. [PERSON] et al. [45] employed a more applicable gradient elasticity theory with the capability of including higher-order parameters and the size effect in the analysis of the instability of the FG cylindrical microshell. Their results confirmed that the radius to thickness ratio and size effect have a significant influence on the stability of the microsystem. Based on the first-order shear deformation theory (FSDT), [PERSON] et al. [46] conducted a numerical study in the dynamic and static stability performance of a composite circular plate by implementing two-dimensional generalized differential quadrature method (GDQM). Moreover, they considered the thermomagnetfield to define the sandwich structure model. As another work, [PERSON] et al. [47] applied DQM in the framework of modified couple stress theory (MCST) to describe stress filed and scrutinize the dynamic stability of an FG boron nitride nanotubes reinforced circular plate. They claimed that using reinforcement in a higher volume fraction promotes the strength and vibration response of the structure. [PERSON] et al. studied the nonlinear oscillation and stability of microcircular plates subjected to electrical field actuation and mechanical force [48]. They concluded that pure mechanical load plays a more dominant role in the stability characteristics of the structure in comparison to the electromechanical load. In addition, they confirmed the positive impact of AC or DC voltage on the stability of the system in different cases of application. To determine the critical angular speed of the spinning circular shell coupled with the sensor at its end, [PERSON] et al. [21] applied GDQM to analyze forced and free oscillatory responses of the structure on the base of thick shell theory. Through a theoretical approach, [PERSON] et al. [49] obtained critical temperature and thermal load of a nano circular shell. [PERSON] et al. [50] introduced a numerical technique with high accuracy to study the static stability, forced, and free vibration performance of a nanosized FG circular shell in exposure to thermal loading. [PERSON] et al. [51] reported the nonlinear dynamic performance of size-dependent circular plates with the piezoelectric actuator in the exposure of a thermal loading with the aid of MCS incorporated with surface elasticity theory to consider the size effects. They highlighted the considerable effect of geometrical nonlinearity on the dynamic characteristics of the system. By employing FSDT, NSGT, DQM, and [PERSON]'s principle, [PERSON] et al. [52] presented a comprehensive parametric investigation in the size-dependent vibration performance of FG circular plate by considering the electro-elastic, thermal and rotational effects. They showed the considerable impact of spinning velocity on the natural frequencies of nanosized systems. In another investigation, the same authors [53] studied the size-dependent vibration response of a spinning two-directional FG circular plate integrated with the piezoelectric actuator (PIAC) based on DQM, [PERSON]'s principle, and FSDT. The results confirmed the high dependency of the dynamic performance of the circular plate to spinning load and externally applied voltage. In the field of structural stability analysis, [PERSON] et al. [54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68] presented buckling and vibrational analysis of the structures with various geometrical parameters.