文章针对钻井工程中钻柱横向振动的实际情况，建立力学模型。
This paper analyzed the practical situation of drilling string lateral vibration during drilling, established mechanical model.
目前对钻柱横向振动的研究基本上忽略了横向振动的激发来源和轴向力的存在。
At present, axial load and excited origin of drilling string lateral vibration is usually neglected.
从理论上分析了轴向载荷存在的情况下钻柱横向自由振动的规律，获得了钻柱横向振动固有频率。
The rule of lateral vibration under axial load was studied in theory, the inherent frequency of drilling string was obtained.
轻微的横向、轴向及扭转振动不影响钻井的正常作业，而钻柱的共振状态会对钻井产生严重的影响。
Light lateral and axis and torsion vibrations do not affect the normal work, but the resonance state has severity effect to drill string.
讨论了初弯曲对钻柱横向非线性振动的影响。
The influence of the initial deflection on the nonlinear lateral free vibration of drill stem is discussed.
在建立牙轮钻头与井底岩石互作用模型的基础之上，建立了基于钻柱和岩石互作用下的牙轮钻头横向振动动力学模型。
On the basis of the interaction model between formation and rock bit, a lateral vibration dynamic model of the rock bit was established under the interaction between drilling string and rocks.
文章研究深井钻柱的振动问题，以深井钻柱为研究对象，分析研究了钻柱的纵向振动、横向振动及扭转振动。
Drill string vibration of deep Wells is studied in the article. The axial vibration, lateral vibration and torsional vibration of drill strings are analyzed.
考虑钻柱的纵向振动、横向振动及扭转振动之间的耦合关系，建立了钻柱振动分析的综合模型。
A general model is developed to analyze drill string vibration considering the coupled relations between longitudinal vibration, lateral vibration, and twisting vibration.
钻柱横向非线性振动的基频随着初弯曲最大挠度的增大而减小，初弯曲对钻柱横向非线性振动基频的影响随钻柱长度的增大而增大，随轴向压力的影响而增加。
The effect of initial deflection on the first frequency increased with either the length of drill stem or the axial compressive force on the drill stem increases.
分析公式表明，钻柱横向线性振动仅是钻柱横向非线性振动的一种特殊情况；
Therefore the nonlinear lateral free vibration of drill stem is investigated by the perturbation method.
分析公式表明，钻柱横向线性振动仅是钻柱横向非线性振动的一种特殊情况；
Therefore the nonlinear lateral free vibration of drill stem is investigated by the perturbation method.
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