Abstract
The method proposed by E.A. Il’yushina is used to study the longitudinal vibrations of segmented buried pipelines. It is shown that the averaged wave velocity in a periodically nonuniform pipeline is specified by the effective static moduli of the periodicity cell and that, in the case of using a vibration damping material made of rubber or soft metal at joints between pipes, this velocity can be much less than the velocity of longitudinal waves in the main pipe. The last fact makes it reasonable to consider supersonic regimes in the problems of seismic vibrations when the wave velocity in a pipeline is less than the wave velocity in the soil.
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References
E. A. IPyushina, “A Version of the Couple Stress Theory of Elasticity for a One-Dimensional Continuous Medium with Inhomogeneous Periodic Structure.” Prikl. Mat. Mekli. 36 (6), 1086–1093 (1972). [J. Appl. Math. Mecli. 36 (6), 1019–1026 (1972)].
R. M. Christensen, Theory of Viscoelasticity: An Introduction (Academic, New York, 1971; Mir, Moscow, 1982).
M. Sh. Israilov, “Seismodynamics of Buried Pipelines,” Problemy Mekhan., No. 3, 18–24 (2012).
G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants (Longmans, London, 1941; Inostrannaya Literatura, Moscow, 1949).
K. Kanai, Engineering Seismology (Univ. Tokyo Press, Tokyo, 1983).
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Original Russian Text © M.Sh. Israilov, 2016, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2016, Vol. 71, No. 1, pp. 68–71.
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Israilov, M.S. A new approach to solve the problems of seismic vibrations for periodically nonuniform buried pipelines. Moscow Univ. Mech. Bull. 71, 23–26 (2016). https://doi.org/10.3103/S0027133016010052
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DOI: https://doi.org/10.3103/S0027133016010052