The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible #uid #ow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the e!ect of viscous structural damping. Linear potential #ow theory is applied to describe the #uid}structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two di!erent boundary conditions are applied to the #uid #ow beyond the shell, corresponding to: (i) in"nite ba%es (rigid extensions of the shell), and (ii) connection with a #exible wall of in"nite extent in the longitudinal direction, permitting solution by separation of variables; they give two di!erent kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the #uid #ow beyond the shell is constrained by rigid ba%es. Results show that the system loses stability by divergence.
where
Poisson's ratio, h the shell thickness, R the mean shell radius, the mass density of the shell, c (kg/m s) the damping coe$cient, and f and p are the radial pressures applied to the surface of the shell as a consequence of external forces and the contained #owing #uid respectivelyS The radial de#ection w is positive inward, RA few words to de"ne &&large'' are useful. In the context of shell theory, large amplitudes signify amplitudes exceeding the shell thickness, or of several times the shell thickness, which in other contexts may be still considered to be small.
SIn this paper, in the calculations presented in section 6, f"0 is taken throughout.