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Dynamics and Stability of a Pipe Conveying Fluid with an Imperfect Inlet Support
Mojtaba Kheiri, Abdolreza Askarian

Last modified: 2018-04-21

Abstract


This paper concerns the dynamics and stability of a pipe conveying fluid supported imperfectly at the inlet and free at the exit. This problem has direct application to, for example, long hanging tubulars used in hydrocarbon storage wells and marine risers in offshore platforms. In reality there is no perfect support. Nevertheless, to date, most studies on the dynamics of pipes conveying fluid assume perfect clamped or pinned ends. It is thus of interest of the present paper to examine the dynamics of pipes conveying fluid with imperfect supports. The focus here will be on the imperfections in the upstream end (or inlet) support. The imperfect support is modelled as a nonlinear torsional spring. Two different types of nonlinear springs are considered: (1) a flat spot type of nonlinearity representing free play in the hinge, and (2) a cubic spring.  The extended Hamilton’s principle for an open system is used to derive the equation of motion of the pipe. The structural dynamics of the flexible pipe is modelled via the Euler-Bernoulli beam theory. On the other hand, the fluid dynamics appear as inertial, Coriolis and centrifugal distributed forces. The resulting equation of motion (i.e. the coupled fluid-structure equation) is spatially discretized using Galerkin’s method where eigenfunctions of a free-free Euler-Bernoulli beam are utilized. A parametric study is performed where the effects of nonlinear springs on the stability boundary of the pipe are investigated.

Keywords


pipe conveying fluid; imperfection; dynamics; stability; nonlinearity

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