Parametric Instability and Snap-Through of Partially Fluid-Filled Cylindrical Shells

The aim of the present paper is to study the parametric instability and snap-through buckling of an axially pre-loaded, partially fluid-filled cylindrical shell. The Donnell non-linear shallow shell theory is used to study the nonlinear vibrations of the shell. For this, the Galerkin method is used, together with a suitable expansion that takes into account the main nonlinear interactions, to discretize the shell. The resulting nonlinear equations of motion are solved by numerical integration. The fluid is assumed to be non-viscous and incompressible and its inertial effects on the shell surface are obtained by the potential flow theory. A detailed parametric analysis is carried out to demonstrate the influence of the fluid height within the shell on the parametric instability load and on the snap-through buckling load in the main parametric resonance region. Using bifurcations diagrams, the main bifurcation events associated with these stability boundaries are identified. The influence of the different types of bifurcation and fluid height on the safety is also discussed.