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Non‐stationary axially symmetric displacement of elastic half‐space in mixed boundary conditions
Author(s) -
Kubenko Veniamin D.,
Yanchevskyi Ihor V.
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000062
Subject(s) - mathematical analysis , mathematics , axial symmetry , hankel transform , half space , laplace transform , displacement (psychology) , boundary value problem , tangent , bounded function , integral transform , domain (mathematical analysis) , geometry , fourier transform , psychology , psychotherapist
The exact solution of the axially symmetric problem concerning the non‐stationary load action on the elastic half‐space surface in the condition of mixed boundary value problem with the given normal stress and tangent displacement on the boundary is obtained. The Laplace and Hankel integral transforms are used. Integral transforms inversion is carried out by means of tabular ratios and convolutions theorems for the wide range of non‐stationary loads. The vertical displacement expression is obtained in the explicit analytical form. The load applied to the bounded dimensions domain is particularly considered. The performed calculations indicate evolution of the elastic displacement in terms of time and space coordinates.