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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 7, Pages 1351–1362 (Mi zvmmf10421)  

This article is cited in 1 scientific paper (total in 1 paper)

Transport solutions of the Lamé equations and shock elastic waves

L. A. Alexeyeva, G. K. Kaishibaeva

Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science of the Republic of Kazakhstan, ul. Pushkina 125, Almaty, 050010, Kazakhstan

Abstract: The Lamé system describing the dynamics of an isotropic elastic medium affected by a steady transport load moving at subsonic, transonic, or supersonic speed is considered. Its fundamental and generalized solutions in a moving frame of reference tied to the transport load are analyzed. Shock waves arising in the medium at supersonic speeds are studied. Conditions on the jump in the stress, displacement rate, and energy across the shock front are obtained using distribution theory. Numerical results concerning the dynamics of an elastic medium influenced by concentrated transport loads moving at sub-, tran- and supersonic speeds are presented.

Key words: elastic medium, Lamé equations, transport loading, Green's tensor, generalized solution, shock wave.

DOI: https://doi.org/10.7868/S0044466916070048

Full text: PDF file (631 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:7, 1343–1354

Bibliographic databases:

UDC: 519.634
Received: 12.05.2015

Citation: L. A. Alexeyeva, G. K. Kaishibaeva, “Transport solutions of the Lamé equations and shock elastic waves”, Zh. Vychisl. Mat. Mat. Fiz., 56:7 (2016), 1351–1362; Comput. Math. Math. Phys., 56:7 (2016), 1343–1354

Citation in format AMSBIB
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\paper Transport solutions of the Lam\'e equations and shock elastic waves
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\vol 56
\issue 7
\pages 1351--1362
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\jour Comput. Math. Math. Phys.
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\vol 56
\issue 7
\pages 1343--1354
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. A. Alexeyeva, “Boundary value problem for elastic half-space by subsonic velocities of surface transport loads moving”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 2:318 (2018), 21–30  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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