Flutter of Conservative Systems of Pipes Conveying Incompressible Fluid

Abstract

An examination of the dynamics of beam-like motions of pipes conveying fluid, with both ends clamped, is presented by means of beam theory and, in the case of thin-walled pipes, by thin-shell theory. Both theories predict that the system loses stability by divergence at sufficiently high flow velocity, and that at higher flow velocity the system is subject to coupled-mode flutter; between the two instabilities there is sometimes a region where the system is completely stable. The critical flow velocities obtained by beam theory and by shell theory are compared, and it is shown that the former coverage towards the latter as the length of the pipe increases.Finally, the existence of coupled-mode flutter in gyroscopic conservative systems, such as the one investigated here, is briefly discussed.