Dependence of frequencies of free oscillations of a thin-walled underground gas pipeline of large diameter on the depth of laying
Abstract
Dependence of frequencies of free oscillations of a thin-walled underground gas pipeline of large diameter on the depth of laying
Incoming article date: 23.09.2019In this paper, the previously obtained equation of motion in displacements is used to determine the frequencies and forms of free oscillations of the underground gas pipeline. The problem of solving this equation is reduced to finding the eigenvalues of the determinant, which are the squares of the natural frequencies of the cylindrical shell. Neglecting the secondary coefficients of the determinant and equating them to zero, the formula for the square of natural frequencies of an underground rectilinear thin-walled gas pipeline exposed to the action of internal working pressure and longitudinal force is obtained, taking into account the reaction of elastic resistance of the soil. Substituting the values for the wave numbers in the longitudinal and circumferential directions into the obtained formula, expressions for determining the frequencies according to the rod and shell theory are derived.Using these expressions, the dependence of the frequencies of free oscillations of the depth of the pipeline at fixed values of the pipe wall thickness, the coefficient of elastic resistance of the soil and the length parameter of the plot, for different values of internal pressure, the ratio of longitudinal compressive forces. When analyzing the results, it was found that with increasing depth of the pipeline, the frequency of free oscillations decreases, and at a certain depth, the frequency of free oscillations becomes equal to zero, this indicates a flattening of the cross section of the pipeline. Using the dynamic stability criterion, for which the frequency of free oscillations turns to zero, an expression is obtained that allows to determine the depth of the pipeline at which the stability loss of the second kind occurs.
Keywords: pipeline, frequency of free oscillations, depth of laying, coefficient of elastic resistance of soil, loss of stability