Abstract
A drill string is a slender structure with nonlinear dynamics; it is an equipment used in the oil industry to drill rock in the search of oil and gas. The aim of this paper is to model the uncertainties related to the speed imposed at the top and uncertainties related to the bit-rock parameters, and to investigate how these uncertainties propagate throughout the system. The continuum system is linearized about the prestressed configuration, the finite-element model is applied to discretize the system, and then a reduced-order model is constructed using normal modes of the linearized system; only torsional and axial vibrations are considered in the analysis. A constant rotational speed is imposed at the top and a nonlinear bit-rock interaction acts at the bottom. A probabilistic approach is used to model the uncertainties and the Monte Carlo method is used to approximate the stochastic differential equations.
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