Coupled seismic vibrations of a pipeline in an infinite elastic medium

Abstract

The exact solution of the problem of coupled seismic vibrations of an underground pipeline and an infinite elasticmediumis given. A method dramatically simplifying the solution of the exterior problem for themedium is proposed on the basis of the established theorem on the separation of the boundary conditions for the wave potentials on the surface of the cylinder. The obtained results permit improving the incorrect consideration of the problem accepted in the literature.

The exact statement of the problem allows one to use the solution of the problem as a test for estimating the accuracy of appropriate approaches and solutions in seismodynamics of extended underground structures.

The results of comparison show that the solutions practically coincide both in the subsonic operation mode (when the seismic wave velocity is smaller than the rod velocity of wave propagation in the pipeline) and in the supersonic operation mode, where a resonance is possible. Thus, the high accuracy of the significantly simpler theory of one-dimensional deformation is confirmed.