A study of the length parameter and the longitudinal compressive forces in the determination of frequencies of free vibrations of thin-walled underground pipelines of large diameter

Earlier work on the study of frequency characteristics of thin-walled underground pipeline to obtain an equation for finding the natural frequencies of the straight sections of the pipeline, taking into account the parameter of the longitudinal force, the magnitude of internal pressure, coefficient of elastic resistance of the soil, the option of thin tubing and added mass of the soil. In this article, using the obtained equation, we study the influence of the length of the section of the pipeline laid in the soil with different physical-mechanical characteristics, and the effect of the parameter of the longitudinal compressive forces at the frequency of free oscillations of thin-walled straight pipeline under the action of various internal working pressure for pipes of different diameters with different wall thicknesses. On the basis of the design data defined in the derived formulae, is determined by the criterion of application of shell theory or the core theory for finding the natural frequencies of thin-walled underground pipelines of large diameter, depending on the length of the element. Simultaneously, the obtained expression allows to determine the critical force at which buckling occurs in the core of the theory («beam buckling»), as well as the formula to determine the critical force, from which buckling occurs by shell theory (flattening of the cross section). Based on these data, it is concluded that flattening the cross section of the pipeline will occur when the force is at times less than required for the formation of «arch release», and consequently to ensure the reliability of underground thin-walled large diameter pipeline should be the first thing to check for resistance on the shell theory.