Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part I: Stability

The study presented is an investigation of the non-linear dynamics and stab ility of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell mot ion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear pote ntial flow theory is applied to describe the fluid-structure interaction. T he system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave r esponse of the shell and shell axisymmetric contraction. Two different boun dary conditions are applied to the fluid flow beyond the shell, correspondi ng to: (i) infinite baffles (rigid extensions of the shell), and (ii) conne ction with a flexible wall of infinite extent in the longitudinal direction , permitting solution by separation of variables; they give two different k inds of dynamical behaviour of the system, as a consequence of the fact tha t axisymmetric contraction, responsible for the softening non-linear dynami cal behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stabili ty by divergence; (C) 1999 Academic Press.