The paper focuses on investigation of resonance regimes of a drill string nonlinear dynamics under the effect of a variable axial compressive force. The drill string is modelled in the form of a rotating elastic isotropic rod with hinged ends. Deformations of the drill string are assumed to be finite. Using Galerkin’s approach a mathematical model of the drill string lateral vibrations reduces to a nonlinear ordinary differential equation for the generalized time function. Applying the harmonic balance method, the amplitude-frequency characteristics of the resonances on basic and higher frequencies are determined. As a result of numerical analysis of the impact of the dynamic system parameters on the resonance curves, considerable nonlinear effects of the amplitude-frequency characteristics of the drill string vibrations are revealed. Recommendations to choose optimal constructive and dynamic characteristics of drill strings are provided.

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