中文摘要：

处于狭长井筒中的钻柱,其动力响应受到钻具组合、内外钻井液流动以及钻井参数等因素的影响,钻柱动力失稳导致的剧烈振动是井壁坍塌和钻具失效的重要原因.考虑到钻杆和钻铤在刚度和线密度上存在很大的差别,论文将钻柱简化为单阶梯输液管柱,钻井液沿着钻柱内部向下泵入并从环空返回地面.耦合考虑钻柱自重、随时间简谐变化的波动钻压、稳定器以及钻井液的水动力和阻尼力,建立了直井中钻柱横向振动的解析模型.利用有限单元法离散为四阶常微分方程后,采用Bolotin法得到临界频率方程确定系统的不稳定区范围,研究了钻压、钻杆长度、稳定器安装位置、钻井液的流速和密度等参数对系统稳定性影响的机理.研究表明：钻压的平均值和波动幅值都是钻柱失稳的驱动因素,而系统的稳定性对处于受拉状态的钻杆的长度变化不敏感.在论文所研究的参数范围内,降低钻井液流速和密度、下移稳定器的安装位置均有助于增强系统的稳定性.

英文摘要：

The dynamic response of a drillstring that is limited in a wellbore is influenced by the bottom hole assembly （BHA）, the drilling fluid inside and outside the drillstring, the drilling parameters, and so on. One of the major causes that lead to hole collapse and drilling tool damage is the severe drillstring vibrations in a state of dynamic instability. It is necessary to study the influences of various parameters, such as the structural parameters and drilling parameters, on the lateral vibrations of drillstring, and to take steps to improve its stability. In this paper, taking into account the big difference between drill pipe （DP） and drill collar （DC）, the drillstring is modeled as a stepped pipe conveying drilling fluid that is pumped down to the bottom inside the drillstring and returns to the ground through the annulus. Mean while, the stabilizer is simplified as a linear spring. For the lateral vibrations of drillstring in a vertical well, an analytical model that considers the drillstring gravity, weight on bit （WOB） varying harmonically with time, arrangements of stabilizer, and hydrodynamic force and damping force of drilling fluid is estab- lished and discretized into the four order ordinary differential equations using the finite element method. The instable regions are determined by solving the critical frequency equation obtained using Bolotin＇ s method. The effects of WOB, length of drillstring, stabilizer location, and velocity and density of drilling fluid on the stability of drillstring system are studied. The results show that both the average value and the fluctuation amplitude of WOB can be the driving factors behind the system instability, and the stability of the system is not sensitive to the length of the drill pipe in tension. Furthermore, reducing the flow rate and density of drilling fluid, and shifting the stabilizer downward are all helpful in maintaining the stability of the system within the parameter ranges discussed in this paper.