It is intended to present dynamic model of the drilling system consists of drillstring and drilling fluid. The drillstring is a sequence of Euler-Bernoulli beam elements with some constraints and loads. Its dynamic model is established by using the absolute nodal coordinate formulas (ANCF). The drilling fluid is composed of three sequences of one-dimensional compressible fluid elements. The three sequences representinternal, annulus and under-bit fluid each. The drilling fluid is modeled by using the Arbitrary Lagrangian-Eulerian (ALE) description, where the force of the drillstring acting on the drilling fluid is introduced through the drilling fluid transport motion, meanwhile, the reaction force acting on the drillstring is taken as an external load. The model also considers the boundary conditions in usual drilling engineering at the bit, at the top, at the connection and at the inner surface of the wellbore.Using this model, the coupled vibration of the drillstring and the effects of the drilling fluid are investigated through several examples.
