Conclusions: In this thesis, the linear and nonlinear dynamic behavior of a multilayer functionally graded graphene platelets reinforced composite cylindrical shells has been studied. Considering the Donnell theory of shells and Von Karman nonlinear hypotheses, as well as applying Hamilton's principle, the governing equations of the shell have been derived. Then, using two methods, Galerkin and differential quadrature, the partial differential equations obtained have been converted into a system of ordinary differential equations in the time dimension. First, the accuracy of the obtained equations and the solution methods has been verified by examining the convergence and comparing the results with existing solutions. Next, to further investigate the accuracy and correctness of the nonlinear equations, the nonlinear equations have been simplified using the Volmir assumption, and then the nonlinear equations have been solved using the multiple scale method. After examining the effects of various material and geometric parameters of the shell on linear and nonlinear frequencies, the dynamic behavior of the cylindrical shell under external force has been studied. First, it is assumed that the shell is under a time-dependent static distributed load, then the behavior of the shell under the moving load has been analyzed as an external moving force. The time response due to the presence of an external load in the linear case was obtained using the Newmark-Beta method with a constant acceleration approach and in the nonlinear case using the fourth-order Runge-Kutta method. The results showed that the geometric parameter of the thickness to radius ratio of the cylindrical shell will have a great influence on the linear natural frequency and with increasing the thickness to radius ratio, the natural frequency values will increase. Also, the lowest natural frequency occurs at lower circumferential mode number. The length to radius ratio of the cylindrical shell is another par