Analysis of Nonlinear Vibrations of a Cylindrical Shell in a Supersonic Gas Flow

Abstract

In the paper nonlinear vibrations of a drill string’s section in a supersonic gas flow are studied. The drill string is modelled in the form of a circular cylindrical shell under the effect of a longitudinal compressing load and torque. In contrast to the previous research, pressure of an unperturbed gas is defined nonlinearly in the third approximation. The eighth order partial differential equation describing the motion of the shell reduces to a nonlinear system of ordinary differential equations with application of the Bubnov-Galerkin technique. An implicit Runge-Kutta method is applied to construct modes of vibrations.