钻柱横向非线性振动分析

以往的钻柱横向振动研究大都忽略了非线性因素， 为此应用摄动法分析了钻柱横向非线性振动， 推导出钻柱横向非线性振动的频率和主振动的一次摄动解公式。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； 非线性因素提高了钻柱横向振动的频率， 改变了主振动的性态， 使其不再成为简谐运动； 非线性因素对频率的影响程度随着振幅、轴向压力和钻柱长度的增大而增加。对于受较大轴向压力作用长钻柱的横向振动， 应当考虑非线性因素的影响。

Nonlinear lateral vibration of drill stem

In the previous study of the lateral vibration of drill stem, the nonlinear factor was ignored. Therefore the nonlinear lateral free vibration of drill stem is investigated by the perturbation method. The first perturbation formulas of frequencies and vibration are derived. An analysis of the formulas shows that, the linear lateral vibration of drill stem is only a special nonlinear lateral vibration, the nonlinear factor results in the increase of the frequency of drill stem's lateral vibration and the variation of the vibration state. The influence of the nonlinear factor on the vibration frequency becomes greater with the increase of the vibration amplitude and axial compressive force and drill stem's length. It is indicated that, in analyzing the lateral vibration of drill stem, the nonlinear factor should be taken into consideration if the stem is long and the axial compressive force is rather large.