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Diffraction of the High-Frequency Waves by Arrays of Obstacles in the Two-Dimensional Elastic Medium, with Multiple Reflections and Transformations

  • Nikolay V. BoyevEmail author
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 109)

Abstract

Within the geometric theory of diffraction, the problem of the propagation of ultrasonic waves through array of obstacles in an infinite two-dimensional elastic medium is investigated. A tonal impulse of a time-harmonic longitudinal or transverse plane elastic high-frequency wave of several wave-lengths is introduced through the array of obstacles, and in a certain domain inside the elastic medium the through-transmitted wave with arbitrary reflections and transformations is received. Some integral representations for displacement in the reflected waves are written out on the basis of the Kirchhoff physical diffraction theory. With the use of an asymptotic estimate of multiple diffraction integrals by the multidimensional stationary phase method we have written out explicitly the geometric-theory approximation for displacements in the multiply reflected and transformed waves.

Notes

Acknowledgements

The present work is performed within the framework of the Project no. 15-19-10008-P of the Russian Science Foundation (RSCF).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Southern Federal UniversityRostov-on-DonRussian Federation

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