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根据钻柱力学和动量守恒基本理论,建立了考虑气体钻井液对钻柱内外耦合影响时的钻柱横向振动模型,此模型与一般的梁式结构的振动模型不同,它包含了钻柱轴力、钻柱内注入压力、环空压力和钻柱内气体对钻柱振动的影响.同时给出边界条件和初始条件.通过把系统外激励函数当作控制变量,利用Banach空间几何性质证明了此系统存在唯一最优控制元.
According to the mechanics of the drill string and the basic theory of conservation of momentum, a model of transverse vibration of drill string considering the influence of gas drilling fluid on the coupling between the inside and the outside of the drill string is established, which is different from the vibration model of a typical beam structure. , The injection pressure in the drill string, the annulus pressure and the influence of the gas in the drill string on the drill string vibration, the boundary conditions and the initial conditions are also given.By using the system extrinsic excitation function as the control variable and using the geometric properties of Banach space, The system has the only optimal control element.