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A Far-Field Asymptotic Analysis in the High-Frequency Diffraction by Cracks

  • M. Y. RemizovEmail author
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 109)

Abstract

On the basis of recently obtained asymptotic solutions of integral equations by the Wiener-Hopf method for diffraction by a straight finite-length crack in a linear elastic medium, we study the properties of the far-zone scattered field at high frequencies for (1) - anti-plane problem in a homogeneous medium, (2) - anti-plane problem for an interface crack, and (3) - in-plane problem in a homogeneous medium.The method proposed is founded on a high-frequency solution of the basic integral equation of the scattering problem. Then we develop an explicit analytical representation for the leading asymptotic term, by estimating the far-field behavior of the relevant integrals with high oscillations by the method of stationary phase. This allows us to obtain the final form of the scattered field in an explicit analytical form as some quadratures.

Notes

Acknowledgements

The author expresses his gratitude to Professor M. A. Sumbatyan, Southern Federal University, Russia, for valuable comments. He would also like to notice that this work has been performed in frames of the project 9.5794.2017/8.9 under support of the Russian Ministry for Education and Science.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematics, Mechanics and Computer ScienceSouthern Federal UniversityRostov-on-DonRussia

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