Spatial Oscillations of a Pipeline on Vibrating Supports under the Action of Variable Internal Pressure

The dynamic behavior of a pipeline on vibrating supports is investigated. A bending-rotational model of spatial displacements of the pipeline is used. The model assumes the absence of deformations that occur when the pipeline axis leaves the bending plane. Therefore, the position of each element of the pipeline on a movable foundation is determined by the displacement of the bend and the angle of rotation of the bending plane around a straight line passing through the supports. In this case, the interactions of internal pressure and changes in the curvature of the axial line, longitudinal, and circumferential deformations of the pipe are taken into account. An estimate of the influence of the amplitude and frequency of the variable internal pressure on the spatial dynamics of the pipeline is given. An approximate analytical solution is obtained for small bending-rotational vibrations of the pipeline. Graphic dependencies of bending and angular displacements of the pipe on time, their phase trajectories, and frequency spectra are shown. An analysis was given and brief conclusions were formulated on the results obtained.