Spatial Nonlinear Oscillations of a Pipeline under the Action of Internal Shock Pressure

Abstract

Spatial nonlinear vibrations of a pipeline section supported at the ends are studied. A pipe bent under both its own weight and constant pressure of the fluid contained therein is subjected to hydraulic shock. The model of bending and rotational motions of the pipeline is used. The gravity forces and the Coriolis (inertia) forces as well as the mutual effect of internal pressure and changes in the curvature of the axial line of the pipe are taken into account. Oscillatory movements of the pipeline are described by a system of two nonlinear differential equations. The first form of oscillation is considered. For an approximate analysis of the dynamics of the pipeline deformation, the inertial and inertial-elastic stages are introduced. At the first stage, only pressure in the fluid and inertial forces are taken into account. The second stage of the bending and rotational motions of the pipeline is a continuation of its inertial stage. At the end of the first stage, the action of the shock load ceases. The Cauchy problem with zero initial conditions is also solved by using the numerical Runge—Kutta method. A comparison of the results of approximate analytical and numerical solutions is given. Changes in the bending of the midpoint of span and the angle of rotation of the steel pipeline are presented as a function of time for different amplitudes of dynamic pressure.