Instabilities of Tubular Beams Simultaneously Subjected to Internal and External Axial Flows

Abstract

This paper examines the dynamics and stability of cylindrical tubular beams conveying fluid and simultaneously subjected to axial external flow. In deriving the equation of small motions, inviscid hydrodynamic forces are obtained by slender-body theory, modified to account for the boundary-layer thickness of the external flow; internal dissipation and gravity effects are also taken into account. Solutions are obtained by means of a method similar to Galerkin’s, with the eigenfunctions approximated by Fourier series. Calculations are presented for tubular beams either clamped at both ends or cantilevered. It is shown that for sufficiently high flow velocities, either internal or external, the system, is subject to divergence and/or flutter. In the case of clamped-clamped tubular beams the effect of the two flows (internal and external) on stability is additive, so that if either flow is just below the corresponding critical value for instability, an increase in the other flow precipitates instability. This is not always the case for cantilevered beams; if the system is just below the threshold of instability due to either flow, instability may be eliminated if the other flow is increased. Experiments conducted with moulded rubber tubular beams in a vertical water tunnel corroborate the theoretically predicted behavior.