: Rotating cylindrical and conical shells are used in many industrial applications, such as drive shaft of gas turbines, rotary kiln and rotor systems. To enhance the stiffness of the shell, it is reinforced by stiffner. Most of these structures are required to operate in a dynamic environment and may have severed vibration, buckling and fatigue phenomena. Therefore, investigating the dynamic characteristics of these structures such as natural frequencies and buckling loads is essentially required. In the present thesis, the analytical solutions for the free vibration, buckling and critical speed of rotating laminated composite cylindrical shell and the free vibration of rotating laminated composite conical shell with longitudinal and circumferential stiffeners are presented. Ritz method and Love’s shell theory are applied in analytical solution. However, in order to analyze the conical shells only the discrete element method is used considering both shell and stiffener geometry. The governing equaion of motion, is evaluted using energy function, then Hamilton ’s principle is applied. For the case of simply-supported shells, the displacement fields can be expressed in terms of the products of sine and cosine functions. As there is no exact solution for other boundary condition, so the GDQ method is used . This method employ an effective way to approach the reliable results using a few numbers of grid point. It should be noted here that is for the first time, the vibration of stiffened rotating conical shells is investigated. Moreover, the vibration equations of the conical shells have not yet been derived using the energy method. In addition, investigation of critical speed, the effects of axial load and internal pressure on the stiffened cylindrical shell was a new topic in this thesis. The effects of parameters such as the shell and stiffeners geometries, fiber’s angles, material, stiffener’s height-to-width ratio, stiffener eccentricity, stiffener material, rotating speed, shell length-to-radius ratio and the number of stiffeners on the natural forward and backward frequencies, buckling load and critical speed is studied. In order to verify the results for cylindrical shell the comparison is made between the present results and those from other authors. Finally, to verify the results of conical shells, the comparison is made in special case where the angle of the conical shell goes to zero.
