An analog of atoms linear chain in seismodynamics of underground pipeline / M. Sh. Israilov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 1. P. 69-72 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 19-21].
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.
Key words: seismodynamics, underground pipeline, analogy of linear lattice.