Geodesic
Transient oscillations of an underground pipeline and soil at inclined fall of a seismic wave
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2022), pp. 50-57

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The coupled unsteady vibrations of an underground pipeline and elastic soil caused by an inclined fall of a plane seismic wave are studied. The coupled self-similar problems are formulated. An analytical solution of the external problem for the soil is obtained. This solution leads to a theoretical expression for the force of interaction between the pipeline and the soil, for which only empirical relations were previously available. Solutions for pipelines in supersonic and subsonic cases demonstrate significantly different behavior, which should be taken into account during earthquake resistance calculations. 
@article{VMUMM_2022_3_a9,
     author = {M. Sh. Israilov},
     title = {Transient oscillations of an underground pipeline and soil at inclined fall of a seismic wave},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {50--57},
     publisher = {mathdoc},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2022_3_a9/}
}
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M. Sh. Israilov. Transient oscillations of an underground pipeline and soil at inclined fall of a seismic wave. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2022), pp. 50-57. http://geodesic.mathdoc.fr/item/VMUMM_2022_3_a9/