Dynamics of fluid-conveying Timoshenko pipes

Abstract

Structures conveying mass lose stability once the mass exceeds a certain critical velocity. The type of instability observed depends on the nature of the supports that the structure has. If the structure (beam or pipe) is cantilevered (thereby deeming it a nonconservative system), “garden-hose-like” flutter instability is observed once a critical velocity is exceeded. When studying the flutter instability of a cantilevered pipe (including shear deformation) by strictly a linear theory, it has been demonstrated through numerical integration that the values of the critical velocity are only valid for small values of the mass ratio (mass of the fluid divided by the total mass) (approximately 0.1 &#946;< ). This fact is also true if shear deformation is neglected. Also, linear theory predicts the pipe to oscillate unboundedly as time progresses, which is physically impossible. Therefore, shortly after the pipe goes unstable, the linear theory is no longer applicable. If non-linear terms are taken into account from the beginning, it can be shown that the pipe oscillates into a limit cycle.