Numerical solution of problem of longitudinal vibration of underground pipeline by the method of finite differences

Abstract

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.