Dynamics and Stability of a Fluid Conveying Vertical Beam

Throughout the oil industry, vertical pipes are used to convey crude oil either offshore from the bottom of the sea or onshore from the depths under the soil. These pipes, otherwise called risers, are attached to a platform at one end and buried under the sea bed or in the ground at the other end. The stability of these pipes is the subject of this investigation. The history of such analysis dates back over five decades when the vibration and stability of fluid conveying Trans-Arabian pipeline network was first studied; albeit for an on-shore environment. For that case, it was found that instability of the flow can be induced by vibration and that if such a horizontal conveyance pipe is supported at both ends, it bows out and buckles when the flow velocity of the conveyed fluid exceeds a critical value. Because of the industrial relevance of such conveyance networks, the problem has continued to generate interest over the years and especially now that deep waters offshore exploration is assuming increased importance in the Oil and Gas sector. When dealing with the stability of these pipes, most workers usually assume the Euler-Bernoulli hypothesis, which requires that plane sections perpendicular to the axis of the beam remain plane and perpendicular both before and after deformation. This essentially means that the deformation of such sections is neglected. However, the Timoshenko hypothesis accounts for such deformation by including transverse shear which is usually neglected. In this paper, the energy method is invoked to derive the governing equations including the effects of external temperature variation along the length of the pre-stressed and pressurized pipe. The stability of such pipes under plug flow model is thereafter presented.