Stability and Non-Linear Dynamics of Clamped Circular Cylindrical Shells in Contact with Flowing Fluid

Abstract

This study presents experimental results on the non-linear dynamics and stability characteristics of a thin-walled clamped-clamped circular cylindrical shell in contact with fluid. It also discusses theoretical results for simply-supported shells conveying inviscid and incompressible fluid. The non-linear Donnell shallow shell theory, with structural damping, is used to describe the large-amplitude shell vibrations. The interaction between the flowing fluid and the shell structure is formulated with linear potential flow theory. The aim of the experimental study was to gather for the first time important data points of the critical flow velocity for instability and maximum flexural displacement, and to analyze the experimental results to validate the theoretical model. The experimental study involved two set-ups: one containing a clamped-clamped silicone rubber shell and flowing air in internal and external flow configurations, and the second an aluminum shell and water as the flowing fluid. The interaction between the shell and the fully developed flow, in both cases, gives instabilities in the form of divergence at sufficiently high flow velocities. The experimental results show a softening type nonlinear behaviour with a large hysteresis in the velocity for the onset and cessation of divergence.