Abstract
This article focuses on the nonlinear effect of the excessive pressure of a supersonic gas flow along with the influence of centrifugal and axial compressive forces on resonance regimes of drill string lateral vibrations. The nonlinear mathematical model of the drill string vibrations is based on Novozhilov’s nonlinear theory of elasticity. The initial curvature of the drill string is also included in the model. Two types of nonlinearities: geometric nonlinearity induced by the drill string finite deformations and the nonlinearity from the gas flow are considered. The Bubnov-Galerkin method is used to derive the equation of motion in generalized parameters. Applying the Fourier series expansion with undetermined coefficients and the harmonic balance method, the amplitude-frequency characteristics for the fundamental frequency and higher harmonics resonance are obtained. A comprehensive numerical analysis of the influence of the drilling system and gas flow parameters on the resonance curves is carried out with the use of the Wolfram Mathematica software package. Visualization of the research results is also provided.