初弯曲对钻柱横向非线性振动的影响

The effect of initial deflection on nonlinear lateral vibration of drill stem

应用摄动法对具有一定初弯曲的钻柱横向非线性自由振动进行了研究。推导出了钻柱横向非线性振动的基频和一阶主振动的一次摄动解公式 ;讨论了初弯曲对钻柱横向非线性振动的影响。结果表明 ,初弯曲对钻柱横向线性振动没有影响 ;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。建议对于具有较大初弯曲且受有较大轴向压力的长钻柱的横向非线性振动应当考虑初弯曲的影响。

In the past study of the lateral vibration of drill stem, the effect of the initial deflection was ignored. For this reason, the nonlinear lateral free vibration of drill stem with initial deflection is investigated by the method of perturbation. The first perturbation formulas of the first frequency and vib ration are derived. The influence of the initial deflection on the nonlinear lateral free vibration of drill stem is discussed. The result shows that, the initial deflection is not the effect on linear vibration of drill stem, the first frequency of nonlinear vibration decreases with the initial deflection of the drill stem increased.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.It is indicated that, in analyzing the nonlinear lateral vibration of drill stem,the initial deflection should be taken into consideration if the initial deflection is larger and the drill stem is longer or the axial compressive force is stronger.