Dynamics and stability of imperfect flexible cylinders in axial flow

Abstract

This paper aims to study theoretically the effects of geometric and support imperfections on the static equilibrium and linear dynamical behaviour of a flexible cylinder in confined axial flow. The support imperfection is modelled via translational and rotational springs at the upstream end of the cylinder while the geometric imperfection is represented by an initially inclined configuration with respect to the fluid flow. The static equilibrium equation is obtained from the principle of virtual work while the equation describing the dynamics of the system around the equilibrium position is obtained using the extended Hamilton’s principle. A central finite difference method and the Galerkin scheme are employed to spatially discretize the static equilibrium equation and dynamic equation of transverse motions, respectively. Numerical results are obtained to show the effects of support and geometric imperfections on the critical flow velocities of the system with various parameters. It is shown that, in general, cylinders with the upstream support imperfection may lose stability at a lower flow velocity compared to the perfectly supported cylinders. It is also shown that the geometric imperfection may have a considerable effect on the dynamic stability of very slender cylinders and those terminated with a perfectly streamlined end-piece.