Effect of Internal Pressure on Parametric Vibrations and Dynamic Stability of Thin-Walled Ground Pipeline Larger Diameter Connect with Elastic Foundation

Abstract

Abstract. The article describes the research methodology of parametric vibrations and dynamic stability of ground thin-walled large-diameter pipeline. The equation of motion of the middle surface of the cylindrical shell element based on elastic resistance of ground. To determine the frequency of free oscillations using the assumptions of the semimomental theory of cylindrical shells and get a complete system of equations for the case of an articulated fixing of the cylindrical shell. Solving the resulting system in analytical form the expression for determining the square of the frequency of free oscillations of a thin-walled ground gas pipeline of large diameter. The methodology of the study of the dynamic stability of a gas pipeline under unsteady effects of internal operating pressure, and the parameter of the longitudinal compressive force, using Mathieu equations. With the help of the Bogolyubov-Mitropolsky techniques built area of dynamic instability in the form of Ince-Strutt diagram for different values of the internal pressure of the pipeline section, the parameter of the longitudinal compressive force, and parameter of thin-walled h / R.

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

“…where ρ0 is the density of the liquid; To solve the problem of frequency characteristics of an large-diameter underground thin-walled oil pipeline, the force equation obtained in [8,9] is used:…”

“…d) with increasing depth of the pipeline and soil pressure q*sl, the value of the length parameter l* increases, that is, the applicability boundary shifts toward the theory of shells; e) with an increase in the added mass of soil, the length l* decreases; f) the longitudinal compressive force parameter P has little effect on the length l* since it reduces the frequencies of free vibrations not only for m=2, n=1 (according to the theory of shells [1][2][3][4][5][6][7][8][9][10]), but also for m=1, n=1 (according to the theory of rods [11,12]).…”

Parametric vibrations of the underground oil pipeline

“…Analysis of works on the problem of dynamic stability of large-diameter main pipelines shows that most of the works on both core and shell theory in this area are devoted to studies without taking into account the influence of the damping properties of the medium. Studies on the core theory were carried out in [1][2][3][4][5][6], on the shell theory -in [7][8][9][10][11][12].…”