An analytical method is presented for the free vibration of a fluid loaded (submerged) ring-stiffened conical shell with variable thickness in the low frequency range. Based on the Flügge theory and equivalent method of ring-stiffeners, the governing equations of vibration of a ring-stiffened conical shell are developed in the form of a coupled set of the first order differential equations. Fluid loading is taken into account by dividing the shell into narrow strips which are considered to be locally cylindrical. Analytical solutions are presented by using the transfer matrix method, which is suitable for structures broken into a sequence of subsystems that interact only with adjacent subsystems. By comparing the results from the present method and the finite element model, good agreement are obtained. The effects of the spacing of the stiffeners, the shell thickness, the shell thickness ratio, the ring's height, and the boundary conditions on the natural frequencies of the fluid loaded ring-stiffened conical shell with variable thickness are discussed.

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