Estimation of Dynamic Loads in Calculations of Aboveground Sections of Gas Pipelines

Abstract

In this paper, the problem of determining the oscillation of the axis of the aboveground part of the gas pipeline laid through the natural obstacle (river, beam, etc.) without intermediate supports, while passing through the purifying piston, is considered. The ends of the area of the gas pipeline in the task are considered to be pinched, taking into account the deflection of the axis of the gas pipeline from its own weight. At the initial moment of time, the land plot of the gas pipeline is stationary. In the composite differential equation for describing the indicated oscillations as their cause, the actual weight of the open section of the gas pipeline and the weight of the mobile cleaning piston are taken into account and the inertial loads are not taken into account. In connection with the movement of the cleaning piston in the differential equation, the Dirac delta function is available. To solve the differential equation of this problem, an integral Laplace transform over time is used. As a result, we obtain an inhomogeneous ordinary differential equation of the fourth order along the coordinate x of the gas pipeline area, which was solved by the method of variation of arbitrary constants. In this case, it was necessary to determine the four functions that were carried out from the boundary conditions of the problem (the absence of deflections along the ends of the gas pipeline and the angles of rotation of their transverse sections), i.e., the solution of the system of four equations satisfying the specified boundary conditions. Next, there was a Laplace transform with a Riemann-Mellin integral. In order to implement the inverse Laplace transform, the terms of direct Laplace transformation were recorded in the form of the product of two pluralities and the original of their product. In this way, the solution of the problem in the form of double integrals is obtained, which allows us to find the displacement of the points of the axis of the gas pipeline section along the entire length of its above-ground part and for any moment of the residence of the cleaning piston in the specified section.