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.

AMS (MOS) subject classification 74K10 74H20 74H25 74H45 65N30.

这项工作的目的是双重的。我们分析了垂直立管横向运动的动力学模型，该立管是石油工业中用于海底钻井作业的长管，在其他情况下是将油从底部带到海面。经过分析，我们提出了一种新的数值方法来求解耦合微分方程组。从数学的角度分析了所提出的模型，该模型中的横向位移与纵向位移相耦合，从中我们证明了所产生的微分方程组的存在性和唯一性。讨论了基于有限元方法的数值模型，并在Matlab代码中成功实现。将数值结果与通过商业计算代码ORCAFLEX（Orcina，2014年）以及实验。在这两种情况下，获得的结果都非常令人满意并且令人鼓舞。

AMS（MOS）主题分类74K10 74H20 74H25 74H45 65N30。