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
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.
elastic medium, Lamé equations, transport loading, Green's tensor, generalized solution, shock wave.
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Computational Mathematics and Mathematical Physics, 2016, 56:7, 1343–1354
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
\by L.~A.~Alexeyeva, G.~K.~Kaishibaeva
\paper Transport solutions of the Lam\'e equations and shock elastic waves
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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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
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