# Free Vibrations and Flutter Analysis of Composite Plates Reinforced with Carbon Nanotubes
## 1 Introduction  
In recent years, there has been a significant increase in the demand for smart, multifunctional materials [1]. Today, incorporating carbon nanotubes (CNTs) into polymer composites results in materials with enhanced mechanical, thermal, and electrical properties due to the structural geometry of the nanotubes. These properties make the resulting composites suitable for multifunctional operations and engineering applications [2, 3, 4, 5]. CNTs are incorporated into a variety of engineering fields, including mechanical and aerospace engineering [6, 7, 8]. CNT/polymer composites are an effective solution for weight reduction, making them a preferred choice in aircraft manufacturing. Due to their unique properties, low-volume fractions of CNT are thought to significantly improve the mechanical properties of nanocomposites. The dispersion of CNTs in a polymer matrix has been shown to increase the mechanical properties of the resulting nanocomposites, even at relatively low weight and volume fractions of CNTs [9]. However, unlike conventional fibrous composites, the length of CNTs is comparable to that of polymer chains. Consequently, the interaction mechanisms between CNTs and the polymer matrix are determined by interfacial chemical bonds, physical forces, and mechanical interlocks, which present significant research challenges [10]. In the context of classical CNT/nanocomposites, thephysical properties remain unchanged at the macroscopic level, regardless of whether the carbon nanotubes are uniformly or randomly distributed within a matrix [2; 3; 4; 11; 12]. In addition to the classical CNT composites, the variation of spatial properties according to a specific non-uniform distribution of carbon nanotubes in functionally graded (FG) materials has also been the subject of considerable attention in the literature [1; 7; 13; 14]. In the dynamic behavior of structures, the overall discussion focuses on a variety of factors that can potentially affect structural behavior, including but not limited to applied aerodynamic theories, boundary conditions, geometry, material properties, and the effects of aero-thermoelastic coupling [5; 15; 16; 17]. The flutter of composite plates in a gas flow is directly related to the instability phenomena that can have a significant impact on the performance of structures such as aircraft structures. Moreover, in the case of CNT/nanocomposites, there is considerable interest in significant damping properties [8; 18]. High structural damping is a critical design parameter, offering the potential to mitigate flutter, reduce gust loading, and extend the fatigue life of structural components. The high aspect ratio combined with the nanoscale dimensions results in a significant interfacial contact area. It is postulated that high frictional energy dissipation occurs during slippage between the nanotubes and the polymer within the nanocomposite [10]. In addition, the ability to increase damping capacity with minimal increase in composite weight is possibly due to the extremely low density of carbon nanotubes. The dynamic instabilities of novel CNT/nanocomposite plates have been the subject of considerable research interest [8; 19; 20; 21; 22; 23]. The literature review shows that dynamic instability analyses mainly consider FG-CNT/nanocomposites with a high-volume fraction of CNTs [7; 14; 19]. Only a few papers consider the uniform or random distribution of nanoreinforcement in a hosting material with low-volume fractions of CNTs [8; 24]. According to the literature review, nanocomposites with small volume fractions of CNT, uniform distribution, and aligned CNT were selected for flutter analysis. The literature review revealed little information about the dynamic instabilities of such nanocomposites. Mostly, the FG nanocomposites with higher volume fractions of CNT were considered in the flutter analysis. For example, [PERSON] et al. [7] considered the FG nanocomposites with 12%, 17%, and 28% CNT volume fractions. [PERSON] et al.