Longitudinal vibrations of underground pipelines of finite length with account for the node weight on the ends

Abstract

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.