Determination of the natural frequencies of the above-ground sections of pipelines transporting an incompressible fluid

Abstract

Under certain conditions, above-ground sections of pipelines are subject to vibration. Increasing the vibration amplitudes beyond the limits can cause the object to fail. In order to assess the vibration resistance of pipelines and to find the most effective ways of detuning from the resonant frequencies of disturbances, it is necessary to determine the natural frequencies of oscillations and the characteristics of the oscillation processes. The authors of the article developed a mathematical model to determine the frequency of free vibrations of above-ground pipeline sections, taking into account the influence of internal pressure and the velocity of the pumped fluid. As a result, a numerical solution based on the Bubnov-Galerkin method was obtained and a sufficient number of series elements in the approximate solution was determined. The authors performed numerical experiments. These showed that the frequencies should be determined for each section under specific conditions according to the pumping mode.