Sapon M. Dynamics of a pipeline with a liquid, which performs rotational motion

This work deals with the study of dynamic processes of a system consisting of a pipeline that performs rotational motion and liquid flowing in this pipeline. In the course of the work, a nonlinear model of the system dynamics was modified for the case of pipeline rotation, which takes into account all nonlinearities except the nonlinearity of the pipeline deformation due to nonlinear rheology. This model provides the conduction of studies in the subcritical and supercritical regions of fluid flow velocity. The dependence of the critical liquid flow velocity on the angular velocity of the pipeline rotation and liquid velocity was determined and it was shown that an increase in the rotation leads to a loss of stability, i.e., to a decrease in the critical flow velocity. The dynamic behavior of the system for different modes of liquid flow and pipeline rotation is investigated. Calculations of testing examples for a variant of a certain constant velocity of liquid flow (angular velocity of pipeline rotation) at different angular velocities of rotation (flow velocities) are performed. It is shown that with the increase of liquid flow velocity (angular velocity of pipeline rotation) at a certain point in time (around the critical velocity) the transition to oscillations around an alternative dynamic equilibrium position with significant manifestation of higher harmonics (additional high-frequency oscillations) around this transition occurs. It is noted also that in the subcritical region the increase in the flow velocity (rotation of the pipeline) leads to a decrease in the frequency of oscillations, in the subcritical region, on the contrary, to an increase. For the modes of linear change of flow velocities (angular velocities of pipeline rotation) it is obtained that the nature of the change of dynamic processes depends on the state of the system at the initial time instant and for motion when the system reaches criticality. For the pulsation modes of fluid flow, which are most interesting due to the fact that the flow in real mechanisms, the pulsation mode occurs, it is determined that the most dangerous are modes with pulsation frequency close to the natural oscillation frequencies of the pipeline and with large pulsation amplitude.