An analogy of linear atom chains in seismodynamics of underground pipelines

In the problem of coupled seismic vibrations of an elastic medium and a segmented pipe supplied with flexible joints, it is drawn an analogy to the linear lattice of concentrated masses. The analogy leads to a simple procedure for studying pipeline seismodynamical problems by reducing the problem for a medium to the one-dimensional one devoted to the shearing vibrations of a cylindrical layer. As examples, the equations for coupled pipeline motions are obtained with consideration of the viscoelastic properties of the medium or the viscoelastic deformation of joints.