Comparison of the bourdon effect and the end cap effect in pipeline vibration analysis

The objects of research are offshore subsea pipelines. Strength, stability and vibration calculations are performed to ensure conditions for their trouble-free and long-term operation. In accordance with the requirements of Rules [1] and [2], a number of factors and loads affecting the pipeline are considered, where it is necessary to take into account the end cap effect, but there are no requirements for taking into account the Bourdon effect. The purpose is to compare the influence of the Bourdon effect and the end cap effect on the free span natural frequency spectrum. For this purpose, using the finite element method, numerical modeling of free spans of various curvatures was performed using two types of finite elements: plate SHELL and tubular PIPE. The former allows to take into account the Bourdon effect directly with or without the end cap effect, while the latter allows to take into account only the end cap effect. As a result of the static structural analysis under the action of internal pressure, the convergence of the plate and tubular models in terms of maximum equivalent stress was obtained, but there is a large difference in deformations, support reactions and buckling eigenvalues, and the tubular model significantly overestimates the latter, which indicates the inadmissibility of its use in assessing global buckling of high pressure pipelines. As a result of the modal analysis, both taking into account and without taking into account the initial stresses from internal pressure, a tendency was revealed for the tubular model to overestimate the values of natural frequencies, although with a difference that fits within the engineering 10 %. Since the use of shell finite elements is associated with a noticeable increase in computational costs, which is not always justified and technically feasible, it is recommended in each specific case to justify the choice of the type of elements, which is possible both through comparative calculations and through safety factors. In general, it has been revealed that the end cap effect is not an equivalent replacement for the Bourdon effect when calculating pipeline buckling and vibration, although it makes it possible to simplify the implementation of the latter through the use of pipe finite elements. 

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