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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.9

ISSN Imprimir: 2152-5102
ISSN On-line: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v28.i1-2.190
pages 258-273

Displacements of the Elastic Half-Space Surface Caused by Instantaneous Axisymmetric Loading

A. G. Kutzenko
Kyiv Taras Shevchenko National University, Ukraine
A. F. Ulitko
Kyiv Taras Shevchenko National University, Ukraine
Valery Oliynik
Institute of Hydromechanics of National Academy of Sciences of Ukraine


General approach to solution of axisymmetric problems on instantaneous loading of an elastic half-space is considered in the present article. Mentioned approach is based on the use of the Laplace's transform with respect to time and the Hankel's transform with respect to spatial coordinate. When originating from analysis of the functions-images it became possible to represent the displacements on the surface of half-space as multiple integrals from functions of real variables. Particular types of loads were investigated, namely, the point load (the Lamb's problem), the Hertz's distribution, and the load arising under the smooth plane stamp in the static contact problem. It has been shown that for any distributed normal load, instantly applied to a boundary of half-space, the normal displacements in an observation point become equal to their static values just after the moment when the Rayleigh's wave generated by a most distant point of the load application passes. Also, the singularities were investigated, arising in a displacement field on fronts of the Rayleigh's waves, which move a from boundary of loading zone. Obtained results give the possibility to make conclusions, useful when considering the non-stationary contact problems.

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