Influence of the Attached Mass of a Transported Gas–Liquid Medium on the Spatial Oscillations of a Pipeline with Vibrating Supports

Spatial vibrations of a pipeline with vibrating supports were investigated. The pipeline transports a gas–liquid medium with an annular structural flow pattern. The flow of particles of a gas–liquid mixture in the cross sections of an accelerated pipeline is taken into account. A comparative analysis of the results of calculations obtained from the analytical solution of linearized and numerical modeling of nonlinear equations of steady-state bending-rotational vibrations of a pipe is given. The influence of the internal attached mass of the transported product on the values of the natural frequencies of the first form of bending and angular oscillations of the pipeline is shown.