Abstarct: In this thesis, the nonlinear vibration analysis of the rotating stiffened truncated conical shells (TCSs) with functionally graded materials (FGM) in a thermal environment under transverse excitation is presented. Also, the resonance analysis of the this shell is performed exposed to a harmonic load. To derive the governing equations of the functionally graded conical shell, classical shell theory baxsed on the Donnell- Mushtari assumptions are used. The effect of stiffener and rotation on the shell is considered in deriving the equations. To add the effect of nonlinear dynamics in the problem, nonlinear von-Kármán relations are used. The effect of rotation around the central axis is considered by assuming Coriolis acceleration and the centrifugal force. To perform the vibration analysis, the partial differential equations are discretized into a set of ordinary differential equations employing Galerkin’s approach. In the theory of classical shells, the static condensation method is used to reduce the equations of motion. First, the frequency analysis and linear vibrations of the system are done and then the nonlinear frequency analysis is examined. To analyze the behavior of nonlinear resonance, the multiple-scale method is used. According to this method, primary, superharmonic, and subharmonic resonances are analyzed for the rotating stiffened truncated conical shell with functionally graded materials. In continue, the governing equations are extracted using the higher-order shear deformation theory (HSDT). Again, utilizing the Galerkin method the ODEs of the system are extracted and free linear vibration, free nonlinear vibration, combination resonance, and primary resonance analysis are examined. In the results section, the effects of the internal and external stiffener, different semi-vertex angles, temperature changes, force changes, volume-fraction index, damping coefficient, and different rotation speeds on the frequency response curve are investigated. In the result section, we can see that increasing of rotating speed and decreasing the semi-vertex angle lead to moving the amplitude-frequency curve to the left and decreasing the hardening behavior for all plots.