## 1 Introduction
Smart control and vibration behavior of viscoelastic laminated sandwich conical shells subjected to hygrothermal loads by using the layerwise theory was proposed by [PERSON] et al. [30]. The shells are made of outer piezoelectric layers with carbon fibers or carbon nanotubes (CNTs) core layers. [PERSON] and [PERSON] [31] presented the viscoelastic dynamic responses of higher order shear deformable FG-CNTRC cylindrical shells subjected to seismic impact in a hygrothermal environment with the Kelvin-Voigt structural damping and the second kind Hankel function of fluid-shell interaction. By using the [PERSON] method, fourth-order Runge-Kutta method and Budiansky-Roth dynamic buckling criterion, the nonlinear dynamic buckling analysis of first-order shear deformable FG-CNTRC cylindrical shells subjected to axial power-law time-varying displacement loads was investigated by [PERSON] et al. [32]. A general approach of free and linear vibration analysis of rotating shear deformable FG-CNTRC cylindrical shells with arbitrary boundary conditions was proposed by [PERSON] et al. [33]. By using the variational differential quadrature method, [PERSON] et al. [34] proposed a unified numerical method on the thermal buckling analysis of higher-order shear deformable FG-CNTRC plates with different shapes, taking into account the temperature-dependent material properties. The magneto-electro-elastic free vibration behavior of a numerical approach of higher-order deformable FG-CNTRC rectangular and skew plates by using the equations of motion and [PERSON]'s principle was developed by [PERSON] [35]. [PERSON] et al. [36] studied the linear buckling and free vibration analysis of a high speed rotating piezoelectric FG-CNTRC cylindrical shell by developing the [PERSON]'s principle, Navier and generalized differential quadrature methods. By using the first order shear deformation theory (FSDT), [PERSON] et al. [37] and [PERSON] et al. [38] investigated the free vibration and buckling behavior of FG-CNTRC truncated conical panels and shells. [PERSON] et al. [39] studied the vibration behavior of SWCNTs/fiber/polymer/metal laminated cylindrical shells with the agglomeration effects of continuously graded single walled carbon nanotubes (SWCNTs) based on the [PERSON]'s first approximation shell theory. Based on the FSDT, [PERSON] et al. [40] presented the elastic behavior of clamped-clamped and short-circuited cylindrical shells with piezoelectric face-sheets and a FG-CNTRC core layer subjected to thermal, electrical, and mechanical loads. [PERSON] et al. [41] investigated the geometrically nonlinear effects of FG-CNTRC classical thin shell panels with surface-bonded active piezoelectric layers while the electric potential linearly varies through the thickness. [PERSON] et al. [42] studied the nonlinear stability and vibration behavior of higher-order shear deformable FG-CNTRC laminated cylindrical shell panels by employing the Galerkin method and the neglect of inertia terms. By combining the sine and exponential power with cosine function, a new higher order shear deformation theory was developed and the linear vibration behavior of FG-CNTRC doubly-curved nanoshells was presented by [PERSON] and [PERSON] [43]. [PERSON] et al. [44] studied the nonlinear buckling of FG-CNTRC beams subjected to uniform temperature rise and angular rotating employing the Timoshenko beam theory and the von Karman nonlinearities. Three-dimensional nonlinear bending behavior of FG-CNTRC plates using the element-free Galerkin method based on the strain-rotation decomposition theorem was investigated by [PERSON] and [PERSON] [45]. [PERSON] [46] studied the linear free vibration analysis of asymmetric sector FG-CNTRC face-sheet sandwich plates with different boundary conditions by using Carrera's unified formulation. Due to the outstanding bearing capacity, the spiral corrugated cylindrical shells are very popular structures in engineering design [47]. In addition, this structure type is suitable with the actual manufacture technologies.