## 1 Introduction  
The extensive field of engineering applications in diverse industries (e.g., automotive, nautical, aeronautics, aerospace) in conjunction with the continuously more demanding design requirements has led to the development of advanced materials capable of addressing their needs, improving their performance, or eliminating deficiencies of conventional materials. For instance, composite materials allow a weight reduction in structural members or machine components without compromising the design requirements. Among these advanced materials, an interesting material known as functionally graded material (FGM) is found, which is basically a material with a variation of mechanical properties along one direction or more. In the literature, it is well known that FGMs were introduced to overcome the limitations of composites, such as delamination at high temperatures due to stress concentrations at interfaces of the composite [1; 2]. The concept of FGM was introduced in the 1980s by a group of scientists in Japan [1; 3; 4]. The available computational resources nowadays, which are very powerful tools for engineers, and the complexities involved in the modeling of new materials have motivated the development of numerical models to predict their mechanical behavior. In the last three decades, researchers have shown increasing interest in the area of FGMs. As mentioned earlier, the functionally graded materials present--in the most general case--a variation of properties through various directions (e.g., along thickness coordinate), and they are usually composed of a mixture of two materials. Therefore, this variation made the FGM a heterogeneous material; due to this fact, different mathematical models,also known as homogenization schemes [5], have been used to evaluate the effective properties of the FGMs, and the gradation of the volume fraction. Several analytic approaches have been proposed, like self-consistent estimates, Mori-Tanaka scheme, [PERSON]'s rule, composite sphere assemblage model, composite cylindrical assemblage model, the simplified strength of materials method, the method of cells, and micromechanical models [5; 6; 7]. Some models that have attracted more attention are [PERSON]'s mixture rule, Mori-Tanaka scheme, and self-consistent models [8]. Generally, the rule of mixture and Mori-Tanaka schemes are used by researchers [3]. The present literature review is limited to those works reporting the free vibration analysis of functionally graded (FG) shell structures, specially those considering a variation of the material properties through the thickness and using a power-law volume distribution of the constituents. Despite this, during the review, free vibration analyses of FG plates with uniform thickness were also found in the works [9; 10; 11; 12; 13; 14; 15; 16; 17], while vibration analyses of FG plates with variable thickness can be found in [18; 19; 20]. Studies related to shells of uniform thickness were presented by [PERSON] [21], [PERSON], [PERSON] and [PERSON] [22], [PERSON] and [PERSON] [23], [PERSON], [PERSON] and [PERSON] [24], [PERSON] et al. [25], [PERSON] et al. [26; 27], [PERSON], [PERSON] and [PERSON] [28], [PERSON] and [PERSON] [29], [PERSON], [PERSON] and [PERSON] [30], [PERSON] [31], [PERSON] et al. [32], [PERSON] et al. [33], [PERSON] et al. [34], and [PERSON] et al. [35]. In the aforementioned works, the formulations are based on different theories such as first-order shear deformation theory (FSDT), third-order shear deformation theory (TSDT), higher-order shear deformation theory (HSDT), wave propagation approach, [PERSON]'s unified formulation, and three-dimensional elasticity theory. Analysis of the free vibration of stepped FG shells was reported by [PERSON] et al. [36] and [PERSON] et al. [37]. Formulations considering the variation of the shell thickness were presented by [PERSON], [PERSON], and [PERSON] [38] for the analysis of FG laminated free-form doubly-curved shells and panels, and by [PERSON] et al. [39] for FG sandwich shell structures.