Vibration and Buckling Analysis of Stiffened Porous Cylindrical Shell with Functionally Graded Coating under Axial Pressure

This study investigates semi-analytical and analytical approaches for analyzing free vibration, as well as nonlinear static and dynamic buckling behavior, of imperfect functionally graded porous cylindrical aluminum shells with functionally graded coatings, subjected to axial compressive stress. The shells are reinforced with stringer and ring stiffeners and are supported by a nonlinear elastic foundation. The governing equations are formulated using classical shell theory and the smeared stiffener technique, incorporating von Kármán–Donnell-type nonlinear terms. Analytical expressions for the static critical stress and natural frequencies are obtained via the Galerkin method, while dynamic responses are determined by using the Runge–Kutta method. The results demonstrate the effects of key parameters—such as porous coefficient, volume fraction index, geometric dimensions, stiffener configuration, and foundation characteristics—on the static and dynamic buckling behavior of the shells.