Influence of the length parameter of an underground oil pipeline on the frequency of free oscillation

Abstract

The problem of finding the natural frequencies of thin-walled underground oil pipelines is solved, based on the application of a semi-momentless theory of cylindrical shells of medium bending, in which bending moments in the longitudinal direction are not taken into account in view of their smallness compared with moments acting in the transverse direction. The solution to this approach is a fourth-order homogeneous differential equation satisfying the boundary conditions of articulation at each end. This equation includes the parameters of the length, internal pressure, thinness of the pipeline, as well as the values of the coefficient of elastic resistance of the soil, the attached mass of the soil and the attached mass of the flowing oil. Based on the data obtained by the derived formulas, the frequency characteristics of large-diameter thin-walled underground oil pipelines are determined depending on the length of the element, as well as on the soil conditions. It has been established that the minimum frequencies are realized for shell modes of vibration with a length parameter of the pipeline section (the ratio of the length of the section to the radius) not exceeding 13. A formula is derived that allows one to determine the boundary between the use of the rod and shell theory for calculating pipelines for dynamic effects. Using the dynamic stability criterion, in which the frequency of natural oscillations vanishes, expressions are derived that allow one to determine the external critical pressure on the wall of the pipeline, which takes into account the length of the pipeline, as well as the number of half waves in the transverse and longitudinal directions, in which the pipeline goes into emergency condition.