A.G.Kutsenko, V.N.Oliynik, A.F.Ulitko Deflections of points of surface of the elastic half-space caused by instant axisymmetric loading |
Acoustic bulletin, Vol. 2 ¹ 2, (1999) |
| There is considered a general approach to solution of axisymmetric problems on instant loading of elastic half-space. Mentioned approach is based on use of Laplas transform with respect to time and Hankel transform with respect to spatial coordinate. Originating from analysis of functions-images it became possible to represent the displacements on surface of half-space in form of multiple integrals from functions of real variables. The particular types of loads were investigated: point load (Lamb's problem), Hertz's distribution and the load arising under smooth plane stamp in static contact problem. It has been shown that for any normal distributed load instantly applicated to boundary of half-space the normal displacements in the point of observation receive their static values just after the moment when Raileygh's wave generated by the most distant point of application of the load passes. Also, the singularities arising in field of displacements on the fronts of Raileygh's waves moving from boundary of area of loading were investigated. Obtained results have given the possibility to make conclusions that will be useful when considering non-stationary contact problems. |
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KEY WORDS: elastic half-space, the Lamb problem, displacement of the boundary, the Rayleigh wave |
| TEXT LANGUAGE: Russian |