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首页> 外文期刊>Fluid mechanics research >Displacements of the elastic half-space surface caused by instantaneous axisymmetric loading
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Displacements of the elastic half-space surface caused by instantaneous axisymmetric loading

机译：瞬时轴对称载荷引起的弹性半空间表面位移

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摘要

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.
机译：本文考虑了一种解决弹性半空间瞬时载荷时轴对称问题的通用方法。所提及的方法是基于时间的拉普拉斯变换和空间坐标的汉克变换的使用。当从对函数图像的分析开始时，就可以将半空间表面上的位移表示为来自实变量函数的多个积分。研究了特定类型的载荷，即点载荷（兰姆氏问题），赫兹分布以及在静态接触问题中在光滑平面压模下产生的载荷。已经显示出，对于任何立即施加到半空间边界上的分布法向载荷，在瑞利波通过最远点产生时，观察点的法向位移就等于其静态值。加载应用程序通过。此外，还研究了奇异性，这些奇异性是在瑞利波前部的位移场中产生的，该位移场从加载区域的边界移动。获得的结果提供了做出结论的可能性，在考虑非平稳接触问题时很有用。

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