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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 3, Pages 478–487
DOI: https://doi.org/10.31857/S0044466922030073 (Mi zvmmf11376) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematical physics

Integral representation of the solution to the nonstationary Lamb problem in the case of a limiting Poisson ratio

H. H. Ilyasova, A. V. Kravtsovb, Al. V. Kravtsovc, S. V. Kuznetsova

a Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, 117526, Moscow, Russia
b Faculty of Physics, Lomonosov Moscow State University, 119992, Moscow, Russia
c National University of Science and Technology MISiS, 119049, Moscow, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466922030073
Abstract: The nonstationary Lamb problem for an elastic half-space with Poisson’s ratio taking a limiting value of $1/2$ is considered. In the axially symmetric case, the solution is represented in the form of a repeated improper integral. The inner integral over the vertical line in the complex plane is reduced to a sum of residues and a sum of several integrals of a real variable. An estimate of the solution is obtained for large values of the polar radius.
Key words: elastic medium, Lamé equations, Poisson's ratio, Fourier–Bessel integral, Laplace transform, estimates of integrals.
Received: 25.06.2021
Revised: 25.06.2021
Accepted: 17.11.2021
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 3, Pages 467–475
DOI: https://doi.org/10.1134/S0965542522030071
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: H. H. Ilyasov, A. V. Kravtsov, Al. V. Kravtsov, S. V. Kuznetsov, “Integral representation of the solution to the nonstationary Lamb problem in the case of a limiting Poisson ratio”, Zh. Vychisl. Mat. Mat. Fiz., 62:3 (2022), 478–487; Comput. Math. Math. Phys., 62:3 (2022), 467–475
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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