This study examines the free vibration behavior of isotropic and fiber-metal laminated cylindrical shells, with and without circumferential ring stiffeners, under clamped-clamped and clamped-free boundary conditions. A semi-analytical formulation based on Flügge thin-shell theory and the Rayleigh-Ritz method is developed and implemented using an in-house Python code to compute natural frequencies. Four FML configurations-aluminum-carbon/epoxy, aluminum-Kevlar-49/epoxy, aluminum-S-glass/epoxy, and aluminum-E-glass/epoxy-are considered to assess the influence of material hybridization. The formulation is validated through finite element modal analysis in ANSYS Workbench, with results showing close agreement and a maximum error below 7%. Carbon-based FML shells show the highest frequency enhancement due to their superior stiffness, while Kevlar and glass-based FMLs provide moderate improvement with favorable stiffness-to-weight characteristics. The inclusion of circumferential ring stiffeners further increases the fundamental natural frequencies, particularly in lower modes. The main contribution of this work is the development of a unified semi-analytical framework that accounts for asymmetric FML configurations, extension-bending coupling, and discrete stiffeners using a Dirac delta formulation within the Flügge-Rayleigh-Ritz approach.
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