Abstract
This paper is based on the equation obtained earlier by V.G. Sokolov to find the frequencies of natural vibrations of straight sections of large-diameter pipelines. In this work, to take into account the effect of hydrostatic pressure on the pipeline wall from oil flowing at different speeds, the solution obtained by M.A. Ilgamov and A.S. Volmyr is used. At the same time, the effect of a stationary fluid flow on the pipeline wall is taken into account in the equation written in forces for the last term of the normal component of inertia forces. The resulting modified equation allows determining the frequency characteristics of the pipeline both according to the rod theory (without taking into account the deformation of the cross section) and according to the theory of shells (taking into account the deformation of the cross section).
Highlights
In the face of increased demand for products from oil refineries, the need for raw materials is increasing
Solving determinant (15), we find the full spectrum of frequencies of free vibrations depending on the wave numbers m and n, as well as the influence of the longitudinal force parameter, the value of the internal pressure, the coefficient of elastic resistance of the soil, the parameter of thinness, the added mass of the soil, the depth of the pipeline and the hydrostatic pressure oil
Let us analyze the influence of the internal working pressure, as well as the coefficient of elastic soil resistance (κ) on the frequencies of free vibrations at fixed values of the parameter of the longitudinal force P, the speed of movement of the oil product through the pipeline V, the parameter of the length of the pipeline L/R and the depth of the pipeline
Summary
In the face of increased demand for products from oil refineries, the need for raw materials is increasing. For a closed cylindrical shell with hinged ends, a solution is proposed in the form of a system consisting of three differential equations of motion in displacements Solving these equations using Fourier series leads to a cubic equation for the square of the circular frequency of free flexural vibrations:. This work raises the question of a new approach to the dynamic calculation of thinwalled underground oil pipelines of large diameter, which is based on the application of the semi-momentless theory of shells of the average bend by Vlasov ─ Novozhilov [20, 21], in which the moments М1, which bend the cylindrical shell in the longitudinal direction, are neglected, since they are much less than the moments М2, which bend it in the transverse direction. The resolving equation of this approach is a homogeneous differential equation of the 4th order, for the solution of which two boundary conditions are used at each end
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