Analysis of the vibration of risers considering coupled longitudinal and transversal displacements and a new numerical approach

The aim of this work is twofold. We analyze a dynamical model for the transversal motion of a vertical riser, which is a long tube used in the petroleum industry for subsea well drilling operations, and in other cases to bring the oil from the bottom to the sea surface. After the analysis, we propose a new numerical approach to solve the resulting system of coupled differential equations. The proposed model, in which transversal displacements are coupled with longitudinal ones, is analyzed from a mathematical point of view, where we proved the existence, and uniqueness for the resulting system of differential equations. A numerical model based on finite element method is discussed and successfully implemented in a Matlab code. The numerical results are compared to those obtained by a commercial computation code ORCAFLEX (Orcina, 2014) and also the experiments. In both situations, the obtained results are very satisfactory and encouraging.

Automated summary

This work aims to analyze a dynamical model for the transversal motion of a vertical riser and proposes a new numerical approach to solve the resulting system of coupled differential equations. The proposed model, in which transversal displacements are coupled with longitudinal ones, is analyzed mathematically with the existence and uniqueness of the resulting system of differential equations proved. The numerical model based on finite element method is successfully implemented in a Matlab code and compared with commercial computation code ORCAFLEX and experiments, showing very satisfactory results.