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利用振型迭加法计算出了钻柱的纵向振动响应，使用改进的Ｒｉｔｚ向量法计算出了整体钻柱的固有频率和固有振型，考虑钻柱沿井深随机分布的接触摩擦阻力作用及泥浆的阻尼作用，提出了钻柱在非对称循环应力状态下的许用持久极限应力的计算公式，建立了钻柱疲劳强度条件，为钻柱动强度计算和安全评定提供理论依据．
The longitudinal vibration response of the drill string was calculated by the modal superposition method. The natural frequencies and natural modes of the whole drill string were calculated by the improved Ritz-vector method. Considering the random contact frictional drag of the drill string along the well depth and the influence of the mud Damping effect, a formula to calculate the permissible ultimate stress of drill string under asymmetric cyclic stress is put forward. The fatigue strength condition of drill string is established, which provides a theoretical basis for calculation and safety assessment of drill string dynamic strength.