Nonlinear dynamics of drill string in horizontal well under axial load and supercritical regime of flowing fluid

In this article, the nonlinear vibration of the spinning pipe conveying fluid in a borehole drilling is investigated under the axial compression load, nonlinear fluid forces, internal and external resonances. The spinning pipe is modeled as a simply supported rotor with imbalance mass and eccentricity. When the flowing fluid is in supercritical regime the pipe oscillates around an equilibrium position in the working frequency range of external excitation. Two to one internal resonance condition between forward and backward natural frequencies of the pipe is found at specific values of flow velocity and rotating speed. The multiple scales method is occupied to solve the governing ordinary differential equations and solvability condition is applied to get the modulation equations. The Runge–Kutta integration and the arc-length continuation method are used for directly solving ordinary differential equations. Bifurcation diagrams are plotted and time responses, phase portraits and Fast Fourier transformation of amplitudes are achieved. The Wolf algorithm is used to determine the Lyapunov Exponents. Periodic, multi-periodic, quasi-periodic, double jump and chaotic behaviors can be seen in simulation results.