气体钻井钻柱轴扭耦合动态屈曲数学建模与求解

Establishment of Extensional-Torsional Coupled Dynamic Buckling Mathematical Model of Drilling String in Gas Drilling and Its Solution

针对钻柱轴扭耦合动态屈曲的基本问题构造哈密顿体系,在辛几何空间中将临界屈曲载荷和动态屈曲模态归结为辛本征值和本征解问题,从而形成一种辛几何算法.方法较好的解决了钻柱轴扭耦合动态屈曲的复杂边界条件问题.在解决气体钻井钻柱动态屈曲问题的研究中具有良好的应用前景.

The paper established the Hamiltonian system to extensional-torsional coupled dynamic buckling of drilling string, the critical buckling load and dynamic buckling modal were come down to sympletic eigen-value and sympletic eigen-solution in symplectic geometry space, consequently, there became a kind of symplectic geometry algorithm, which can resolve better the complex boundary conditions of extensional-torsional coupled buckling of drilling string, there have good application prospects to solve dynamic buckling of the drill string in gas drilling.