Mathematical modeling of the transmission pipeline under the influence of earthquake seismic waves

Abstract

The stress-strain state of an underground transmission pipeline under the action of earthquake seismic waves is considered. The main objective of this study is the construction of a mathematical model with the analytical solution for lower estimation of the influence of earthquake seismic waves on the transmission pipeline. The spectra of the design seismic actions of the earthquake are determined on the basis of parameters of real seismograms of past earthquakes. The generalized functions of seismic impulses are constructed. The transmission pipeline is modeled by a thin bar. Equations of pipeline motion using the Laplace transformation in time are solved, stresses are determined. The numerical example is considered. The results of calculations on the theories of Kirchhoff and Timoshenko are compared. Graphs of stress changes depending on the earthquake’s strength in points are given. The limiting value of the earthquake magnitude resulting in large stresses and deformations is determined. As a result, the transmission pipeline is destroyed.