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., 2022, Volume 62, Number 3,Pages <nobr>478

This article is cited 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. Ilyasov^a, A. V. Kravtsov^b, Al. V. Kravtsov^c, S. V. Kuznetsov^a

^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

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.

UDC: 519.634

Received: 25.06.2021
Revised: 25.06.2021
Accepted: 17.11.2021

DOI: 10.31857/S0044466922030073