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The article presents an analysis of the dynamic response of an underground main pipeline under the action of a longitudinal wave, propagating in soil along the pipe. It is assumed that the elastic pipe has a finite length. A linear viscoelastic model of the "pipe-soil" system interaction is considered. The influence of a pulse in the form of a triangle on the deformed state of an underground main pipeline is investigated. The article presents a comparative analysis of the results obtained for some values of the coefficients of elastic and viscous interaction, the propagation velocity, and the duration of the pulse. In the case of elastic interaction of the "pipe-soil" system, the reflection of the wave propagating in the underground pipeline on the boundaries of the pipeline when it coincides with the wave propagating in the soil leads to an increase in the maximum deformation of the underground pipeline, the value of deformation can double. The viscosity coefficient of interaction at the pipe-soil system contact leads to the wave front attenuation in the underground pipeline. For soils with the coefficient of viscous interaction higher than 100 kN∙s/m2, this leads to complete attenuation of the bursts at the wave front in the pipeline. The influence of the wave propagation in soil on the deformation values at the wave front was also studied.

This paper analyzes the dynamic response of a wave propagating to the soil horizontally through a pipe. That is, the state considers a linear viscoelastic model of the interaction of the "pipe-soil" system. This problem is solved using the numerical method of differential equations. The longitudinal wave in the ground is taken as a sinusoid. And also, in the article, we will compare the comparative analysis of the results for some values of the coefficients of elasticity and viscosity of taste, propagation velocity, and pulse duration. In the current flow of the "pipe-soil" system, reflections of waves propagating in an underground pipeline at the boundaries of the pipeline, usually propagating in soils. This leads to a change in the shape of the underground pipeline, the value of which can double. The viscosity coefficient of interaction at the "pipe-soil" system contact leads to attenuation of the wave front in the underground pipeline. For soils with values of viscous interaction coefficient more than 100 kN·s/m2, this may lead to complete attenuation of the bursts at the wave front in the pipeline. The ratio of steps along the coordinate and time equal to the propagation of waves in the pipeline, obtaining results that coincide with the exact nature.

The paper presents an analysis of the dynamic response of an underground main pipe under the action of longitudinal wave, propagating in soil along the pipe. The outer surface of the pipeline is in contact with soil along the pipeline axis according to the elastic- viscous law, and the ends of the pipeline are connected to massive nodes by elastic elements. Using the Fourier method, an analytical solution to the problem of longitudinal vibration of an underground pipeline, pliantly fixed by nodes at its ends, is obtained. The problem of longitudinal vibration of an underground pipeline with visco-elastically fixed nodes at the ends is solved numerically. Longitudinal wave in soil is taken as a traveling sine wave. The paper presents a comparative analysis of the results for some values of seismic wavelengths, the ratio of the wave propagation velocity in soil and in the pipeline, the coefficients of elastic and viscous interaction. The viscosity coefficient of interaction at the "pipe-soil" system contact leads to attenuation of the wave front in the underground pipeline. For soils, the values of the viscous interaction coefficient of more than 100 kN⋅s/m2, may lead to complete attenuation of the bursts at the wave front in the pipeline.

An analysis of the dynamic response of an underground main pipeline under a longitudinal wave propagating in soil along the pipe is given in the article. The problem of the longitudinal wave impact on a pipeline of finite length, interacting with soil according to the elastic-viscous law, is considered. The ends of the pipeline are fixed to massive nodes that interact with the medium according to linear laws. Along the length of the pipeline, the coefficients of the elastic and viscous pipeline-soil interaction change depending on the coordinate. In this article, the influence of the coefficients of elastic and viscous interaction of the "pipe-soil" system is studied when these coefficients are coordinate functions. The variability of the values of the coefficients along the length of the pipeline leads to a change in displacements from 0 to 15% and strain from 0 to 18%, compared with the case when these coefficients are constant. Depending on the length of the pipeline, the response of the pipeline to seismic action is different. This is especially evident at the boundary points. Considering the weight of nodes leads largely to a decrease in the strain of the pipeline relative to the soil strain at the boundary points.