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国内外在研究钻柱振动时都把钻柱下端当作铰支，假设激振源为周期性的，偏离实际。从建立符合实际的下端边界 条件入手，着重研究了钻柱的纵向振动。用有限单元法，求出整体质量、整体刚度，整体阻尼矩阵采用的是比例阻尼矩阵， 利用牛顿法得到钻柱的振动方程，另外通过钻头与岩石的相互作用模型得到了真实的钻柱下端边界条件，并利用Ｈｏｕｂｏｌｔ 数字解法模型求解了振动微分方程。根据上述模型编制了用于分析钻柱纵向振动的计算机仿真软件，并进行了大量仿真 实验，通过对实验结果分析得到了有意义的结论。
At home and abroad, the lower part of the drill string is regarded as a hinge when studying the vibration of the drill string. It is assumed that the excitation source is periodic, deviating from the actual situation. Starting with the establishment of a realistic lower boundary condition, the longitudinal vibration of the drill string is emphasized. Using the finite element method, the overall mass and the overall stiffness are obtained. The damping matrix of the whole damping matrix is proportional damping matrix. The vibration equation of the drill string is obtained by Newton’s method. The lower bound of the drill string is obtained by the interaction model between the drill bit and the rock Conditions, and using Houbolt digital solution model to solve the vibration differential equation. According to the above model, the computer simulation software for analyzing the longitudinal vibration of the drill string was compiled and a large number of simulation experiments were carried out. The meaningful conclusions were obtained by analyzing the experimental results.