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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 7, Pages 1351–1362
DOI: https://doi.org/10.7868/S0044466916070048 (Mi zvmmf10421) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
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DOI: https://doi.org/10.7868/S0044466916070048
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.
Received: 12.05.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 7, Pages 1343–1354
DOI: https://doi.org/10.1134/S0965542516070046
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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