采用研究连续系统振动问题的分析方法，对深水钻井隔水导管建立其弹性体连续系统的振动二阶偏微分方程。该方程考虑了隔水导管作为均质连续弹性体，在轴线方向上所受的作用力及约束条件，包括在海床井口处的约束、隔水导管张力器影响以及钻井平台在竖直方向上因波浪升沉而产生的影响。建立了杆件的纵向振动微分方程，并求解得出了隔水导管纵向振动的频率方程。研究结果显示，深水钻井隔水导管的纵向振动频率与隔水导管的截面面积、管体的杨氏模量、体积质量、隔水导管张力器的弹簧系数、波浪运动的波高、水深等6个主要参数有关。以上研究对于深入理解隔水导管的纵向振动特性，科学指导钻井作业具有重要的实践意义。

This paper employs an analytical approach to study vibration problems in continuous systems. For the riser in deep-water drilling， a second-order partial differential equation for the vibration of its continuous elastic system is established. This equation considers the forces and constraints acting on the riser as a homogeneous continuous elastic body along its axial direction， including constraints at the seabed wellbore， the influence of the riser tensioner， and the vertical heave motion of the drilling platform due to waves. Based on this， a differential equation for the longitudinal vibration of the rod member is further developed， and the frequency equation for the longitudinal vibration of the riser is solved. The research results indicate that the longitudinal vibration frequency of the deep-water drilling riser is related to six main parameters： the cross-sectional area of the riser， the Young's modulus of the pipe body， the volumetric mass， the spring coefficient of the riser tensioner， the wave height of wave motion， and the water depth. This study has important practical significance for gaining a deeper understanding of the longitudinal vibration characteristics of the riser and scientifically guiding drilling operations.