In this work, the influence of the characteristic geometric parameters of a cylindrical shell, such as radius-to-thickness and radius-to-length ratios, on both the linear and non-linear vibrations of a fluid-filled cylindrical shell with internal flowing fluid is studied. The Donnell non-linear shallow shell equations are used to study a simply supported cylindrical shell subjected to both lateral and axial time-dependent loads with internal flowing fluid. The fluid is assumed to be inviscid and incompressible and the flow isentropic and irrotational. An expansion with eight degrees of freedom, containing the fundamental, companion, gyroscopic and five axisymmetric modes is used to describe the lateral displacement of the shell. The Galerkin method is used to obtain the nonlinear equations of motion which are, in turn, solved by the Runge-Kutta method. First, the parametric linear equations are used to study the influence of geometry and physical properties on the natural frequencies, critical flow and critical circumferential wavenumber. Secondly, numerical methods are used to describe the influence of geometric characteristics on the non-linear frequency-amplitude relations of the shell. The results obtained show the influence of the geometric parameters on the vibration characteristics of the shell and can be used as a basic tool for design of cylindrical shells in a dynamic environment.

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