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IssuesArchive of Issues2018-3pp.340-348

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M.Sh. Israilov, "Analogy of a Linear Chain and Seismic Vibrations of Segmental and Viscoelastic Pipelines," Mech. Solids. 53 (3), 340-348 (2018)
Year 2018 Volume 53 Number 3 Pages 340-348
DOI 10.3103/S0025654418070129
Title Analogy of a Linear Chain and Seismic Vibrations of Segmental and Viscoelastic Pipelines
Author(s) M.Sh. Israilov (Chechen State University, ul. A. Sheripova 32, Groznyy, 364024 Russia, israiler@hotmail.com)
Abstract In the problem of seismic vibrations of a segmental pipeline with damping joints, deformed by the law of linear viscoelasticity, an original analogy with a linear chain of concentrated masses was put forward. The constructed discrete system generalizes the monatomic lattice model in the sense that the viscoelastic interaction between the masses of the chain is considered and, moreover, the forced (and not own) oscillations of such a system are investigated. By the transition from a discrete system to a continuous one, the integro-differential oscillation equation of a segmented pipeline with viscoelastic joints in an elastically resisting medium is obtained. This equation is a generalization of the well-known Klein-Gordon differential equation describing the "constrained" vibrations of an elastic rod or string in a medium with elastic resistance. In addition, the equation gives the problem of seismic vibrations of a continuous pipeline from a polymer (viscoelastic) material.

Joint stationary seismic vibrations of a viscoelastic pipeline and soil were studied in an exact formulation and maximum stresses in the pipeline were found by solving the resulting integro-differential equation. The same stresses were found using the "hard pinch" engineering approach, according to which displacements and deformations in the seismic wave and pipeline are the same. By analyzing the stresses found under the viscoelasticity law in the form of the Kelvin-Voigt model relationship, it is established that the generally accepted position that the engineering approach gives an upper estimate for the stresses in the pipeline is valid only in the subsonic case (when the seismic wave velocity is lower than the wave velocity in the pipeline) and is not valid in the supersonic mode, when the exact theory can lead to stresses exceeding those calculated on the basis of the engineering approach.
Keywords segmental and polymer pipelines, seismic vibrations, linear chain analogy
References
1.  M. J. O'Rourke and X. Liu, Response of Buried Pipelines Subject to Earthquake Effects (Multidisciplinary Center for Earthquake Engineering Research (MCEER), Buffalo, 1999).
2.  M. Sh. Israilov, "An Analogy of Linear Atom Chains in Seismodynamics of Underground Pipelines," Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 1, 69-72 (2015) [Moscow Univ. Mech. Bull. (Engl. Transl.) 70 (1), 19-21 (2015)].
3.  A. C. Eringen, Mechanics of Continua (John Wiley&Sons, New York, 1967).
4.  N. N. Lebedev, Special Functions and Their Applications (Fizmatgiz, Moscow, Leningrad, 1963) [in Russian].
5.  L. Brillouin and M. Parodi, Propagation des Ondes dans les Milieux Périodiques (Masson, Paris, 1956; Izdat. Inostr. Liter., Moscow, 1959).
6.  F. Omori, "Seismic Experiments on the Fracturing and Overturning of Columns," Publication of the Earthquake Investigation Committee in Foreign Languages. No. 4, 69-141 (1900).
7.  Sh. G. Napetvaridze, Seismic Resistance of Hydraulic Structures (Gosstroyizdat, Moscow, 1959) [in Russian].
8.  N. H. Newmark, "Problems in Wave Propagation in Soil and Rock," in Proc. of the Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials (Univ. of New Mexico Press, New Mexico, 1968), pp. 7-26.
9.  Standards for the Design of Nuclear Power Plants: NP 031-01. Appendix 6. The Main Provisions of the Calculation of Linearly Extended Structures (Moscow, 2001) [in Russian].
10.  D. V. Georgievskii and M. Sh. Israilov, "Seismodynamics of Extended Underground Structures and Soils: Statement of the Problem and Self-Similar Solutions," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 138-151 (2015) [Mech. Solids. (Engl. Transl.) 50 (4), 473-484 (2015)].
11.  M. Sh. Israilov, "Coupled Seismic Vibrations of a Pipeline in an Infinite Elastic Medium," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 57-66 (2016) [Mech. Solids. (Engl. Transl.) 51 (1), 46-53 (2016)].
12.  B. B. Prasad, Fundamentals of Soil Dynamics and Earthquake Engineering (PHI Learning, Delhi, 2013).
13.  D. E. Gray (Editor), American Institute of Physics Handbook, 2-d ed. (McGraw-Hill, New York, 1963).
14.  M. Sh. Israilov, "Seismodynamics of the Underground Pipeline," Probl. Mekh. AN RUz. No. 3, 18-24 (2012).
15.  M. Sh. Israilov, "Related Problems of Pipeline Seismodynamics," Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 5, 41-45 (1996).
Received 05 December 2016
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