Nonstationary loading at the elastic half-space surface

Authors

  • V.D. Kubenko

DOI:

https://doi.org/10.15407/dopovidi2014.05.058

Keywords:

elastic half-space, loading, surface

Abstract

A nonstationary stress is applied to the surface of an elastic half-space. It is necessary to built a solution of the transient boundary problem and to determine the stress-strain state of the half-space. The solution is realized with help of the Laplace and Fourier integral transformations. The coupled inversion of the integral transforms is realized. As a result, the exact solution for a stress and a displacement along the axis of symmetry of the problem is determined. Numerical examples are given.

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References

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Guz A. N., Kubenko V. D., Cherevko M. A. Diffraction of elastic waves. Kyiv: Nauk. dumka, 1978 (in Russian).

Bateman G., Erdeyi A. Tables of integral transformations. In 2 vols. Vol. 1. Fourier transforms, Laplace transforms, Mellin transforms. Moscow: Nauka, GIFML, 1969 (in Russian).

Cagniard L. Reflexion et Refraction des Ondes Seismiques Progressives. Paris: Gauthier-Villars, 1939.

Slepyan L. I. Nonstationary elastic waves. Leningrad: Sudostroenie, 1972 (in Russian).

Ditkin V. A., Prudnikov A. P. Integral transforms and operational calculus. Moscow: GIFML, 1961 (in Russian).

Kubenko V. D. Dopov. Nac. akad. nauk Ukr., 2011, No. 10: 67–71 (in Russian).

Published

25.02.2025

How to Cite

Kubenko, V. (2025). Nonstationary loading at the elastic half-space surface . Reports of the National Academy of Sciences of Ukraine, (5), 58–64. https://doi.org/10.15407/dopovidi2014.05.058