Investigation of the frequency of free vibrations for pipelines with different physical and mechanical properties of the material

Abstract

This paper raises the question of a new approach to the dynamic calculation of thin-walled underground pipelines of large diameter, which is based on the application of the Vlasov-Novozhilov half-time theory of medium-bend shells, which ignores the M1 moments that bend the cylindrical shell in the longitudinal direction, since they are much smaller than the M2 moments that bend it in the transverse direction. The resolving equation for this approach is a homogeneous 4th-order differential equation that uses two boundary conditions at each end to solve it. The resulting equation takes into account the parameter of the longitudinal force, the value of the internal pressure, the coefficient of elastic resistance of the soil, the parameter of thinness, as well as the attached mass of the soil. Based on the data obtained from the derived formulas, the frequency characteristics of thin-walled underground pipelines of large diameter with different physical and mechanical properties are determined depending on the length of the element, as well as ground conditions. It is established that the minimum frequencies for the shell form of vibrations in various ground conditions are realized only for steel pipes, and for polyethylene and fiberglass pipes, depending on the coefficient of elastic resistance of the soil, they can be realized both in the rod and shell form. At the same time, using a dynamic stability criterion, derived expressions to determine the critical external pressure, taking into account the pipe length and the number of half waves in the cross section in which there is a constructive denial of the pipeline. Based on this expression, a formula for determining the critical depth of laying for thin-walled pipelines is obtained.