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在现有三维空间钻柱力学基本方程的基础上 ,考虑横向剪应力和剪应变两因素对钻柱挠曲变形的作用 ,参照S P Timoshenko剪切梁理论 ,针对空间钻柱受力与变形特征 ,引入 ψN 和ψB2个广义位移函数 ,建立了钻柱力学剪变形理论的通用基本方程。以某水平井一单跨钻柱两端简支情况下的二维横向振动为具体算例 ,给出了计算公式。该公式综合描述了横向剪切变形和轴向钻压对钻柱横向振动固有频率的影响 ,是对现有钻柱力学基础理论的补充和完善
Based on the existing basic equations of drill string mechanics in the existing three-dimensional space, considering the effect of transverse shear stress and shear strain on the flexural deformation of drill string, according to the SP Timoshenko shear beam theory, according to the stress and deformation characteristics of the drill string, The ψN and ψB2 generalized displacement functions are introduced, and a general basic equation of the deformation theory of drill pipe mechanical shear is established. Taking a two-dimensional transverse vibration of a single horizontal cross-sectioned drill string at both ends simply supported as a practical example, the calculation formula is given. The formula comprehensively describes the influence of transverse shear deformation and axial weight on the natural frequency of transverse vibration of drill string, which is a complement and improvement to the existing basic theory of drill string mechanics