## 1 Introduction  
Due to many excellent mechanic properties, functionally graded material (FGM) has been popularly applied in engineering designs, such as military systems, nuclear reactors, civil engineering and other technologies. Static and dynamic behavior of FGM cylindrical shells is the problem which is especially a focus by many authors. [PERSON] [1; 2] studied the postbuckling behavior of FGM cylindrical shells in a thermal environment subjected to axial compressive and radial loads. The stability equation system was established by using the Donnell shell theory and the von Karman nonlinearities combined with the prebuckling deformations and the geometrical imperfection. Nonlinear buckling behavior of higher-order shear deformable piezolaminated cylindrical shells subjected to radial pressure loads taking into account the temperature dependent effects of materials and geometrical imperfection was presented by [PERSON] and [PERSON] [3]. By using the energy method, [PERSON] and [PERSON] [4; 5] studied the linear and nonlinear buckling behavior of imperfect and perfect FGM cylindrical shells subjected to axial compressive loads. [PERSON] and [PERSON] [6] and [PERSON] [7; 8; 9; 10] investigated the linear and nonlinear buckling and vibration behavior of FGM cylindrical shells and FGM truncated conical shells subjected to static and dynamic loads with different boundary conditions. By using the Lord-Shulman and Maxwell formulations, [PERSON] et al. [11] presented a thermoelastic approach to investigate the wave propagation of piezoelectric FGM cylindrical panels subjected to the thermal shock loads. [PERSON] et al. [12] investigated the nonlinear buckling of higher-order shear deformable FGM cylindrical shells surrounded by two-parameter Pasternak's elastic foundation subjected to combined axial and radial compressive loads. [PERSON] et al. [13] studied the dynamic buckling behavior of higher-order shear deformable FGM porous cylindrical shells with even and uneven porosity distribution types. [PERSON] and [PERSON] [14] discussed the frequency responses of perforated shells with uncertain materials and damage by using the higher-order finite element method. Nonlinear buckling behavior of large deflection FGM and porous-core FGM spiral stiffened cylindrical shells subjected to axial compressive, radial and torsional loads with and without elastic foundation by using the improved [PERSON]'s smeared stiffener technique and the [PERSON] method was studied by [PERSON] et al. [15; 16; 17; 18; 19]. Based on genetic algorithms and neural networks, [PERSON] and [PERSON] [20] maximized the eigenfrequency gaps of laminated composite cylindrical shells. Carbon nanotube-reinforced composite (CNTRC) is an advanced material which has gained particular interest in recent years. The postbuckling behavior of CNTRC cylindrical shells subjected to radial pressure, axial compression and torsion with temperature effects was investigated by [PERSON] [21; 22; 23]. Two types of CNTRC, namely, uniformly distributed CNTRC (UD-CNTRC) and functionally graded CNTRC (FG-CNTRC) were discussed. By employing the boundary layer theory and the singular perturbation technique, [PERSON] and [PERSON] [24] investigated the postbuckling behavior of FG-CNTRC cylindrical shells with and without elastic foundation subjected to the combined axial compressive and radial loads in a thermal environment. Linear buckling behavior of first order shear deformable FG-CNTRC truncated conical shells subjected to radial loads was estimated by [PERSON] and [PERSON] [25] based on the linear membrane analysis and the adjacent equilibrium criterion. [PERSON] et al. [26; 27; 28] studied the linear free vibration and dynamic responses of FG-CNTRC conical shells, cylindrical panels and skews cylindrical shells. [PERSON] et al. [29] investigated the thermal and moisture effect on the dynamic responses of a submerged viscoelastic agglomerated carbon nanotube (CNT) cylindrical shell subjected to earthquake loads.