Geodesic
A new approach in the problems on seismic oscillations of periodically inhomogeneous underground pipelines
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 68-71

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The longitudinal vibrations of segmented buried pipelines are studied by E.A. Ilyushina's method. It is shown that the “averaged” wave velocity in a periodically inhomogeneous pipeline is defined by the effective static moduli of its cell and that, in the case of the use of rubber or soft metal layings at joints, this velocity may be rather less than the velocity of waves in the basic pipe. The last circumstance justifies the inclusion of the supersonic case (the case for which the wave velocity in a pipe is less than the wave velocity in the soil) into the formulation of the problems devoted to seismic vibrations. 
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     author = {M. Sh. Israilov},
     title = {A new approach in the problems on seismic oscillations of periodically inhomogeneous underground pipelines},
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M. Sh. Israilov. A new approach in the problems on seismic oscillations of periodically inhomogeneous underground pipelines. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 68-71. http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a13/