The drilling operations use a rotary slender structure introduced inside the drill well. The nonlinear dynamics with bit-bouncing, stick-slip phenomena, and pulsating mud flow may yield the premature wear and damage of drilling equipment and should be investigated to improve the reliability of drilling operations. This work presents the beam element formulation to model the drilling nonlinear dynamics. The well-pipe contacts are modeled by the radial elastic stops. The fluid–structure interactions are considered. The first step consists in computing the static position of structure to determine the contact points and calculate the preloaded state. These results are then considered to calculate the Campbell diagram. The potentially unstable speeds of rotation are identified. The results show that the modal coupling phenomena strongly occur for the three-dimensional well. The well-pipe contacts modify the modes in rotation, and the rotating fluid induces a strong deviation of the flexural mode curves.

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