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In this paper, free vibration analysis of rotating functionally graded cylindrical shells with orthogonal stiffeners is presented. Based on Love's first approximation theory and smeared stiffeners technique, the governing equations of motion which take into account the effects of initial hoop tension and also the centrifugal and Coriolis forces due to rotation are derived. The influence of the power law index, the stiffener's height-to-width ratio, the circumferential wave numbers, the shell length-to-radius ratio, and the shell radius-tothickness ratio on the natural frequencies of the simply supported rotating stiffened functionally graded cylindrical shell are investigated. To validate the present analysis, comparisons are made with those available in the literature for particular cases; very good agreements are achieved.

In this paper, the analytical solution for static and vibration analysis the cross-ply laminated composite doubly curved shell panels with stiffeners resting on Winkler-Pasternak elastic foundation is presented. Based on the first-order shear deformation theory, using the smeared stiffeners technique, the motion equations are derived by applying the Hamilton's principle. The Navier's solution for shell panel with the simply supported boundary condition at all edges is presented. The accuracy of the present results is compared with those in the existing literature and shows good achievement. The effects of the number of stiffeners, stiffener's height-to-width ratio, and number of layers of cross-ply laminated composite shell panels on the fundamental frequencies and deflections of stiffened shell with and without the elastic foundation are investigated.

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