On the 3D elastic wave propagation through a cascading system of three doubly-periodic arrays of co-planar cracks

Authors

  • Sumbatyan M.A. South Federal University, Rostov-on-Don, Russian Federation
  • Remizov M.Yu. South Federal University, Rostov-on-Don, Russian Federation

UDC

539.3

EDN

YRMLED

DOI:

10.31429/vestnik-15-4-40-53

Abstract

The paper is devoted to the calculation of the reflection and transmission coefficients, when a plane wave is incident on a three-dimensional system of three parallel doubly-periodic gratings of rectangular cracks in the elastic material. In the one-mode frequency range the problem is reduced to a system of integral equations holding over the single chosen crack. The semi-analytical method previously introduced for three-dimensional scalar and two-dimensional elastic problems gives an explicit representations for the wave field and the scattering parameters.

Keywords:

double-periodic crack array, low-frequency mode, integral equation, transformation of hypersingular integral equation kernel, semi-analytical method, reflection and transmission coefficient, acoustic filter

Funding information

Исследование выполнено при финансовой поддержке Российского научного фонда (проект № 15-19-10008-П).

Authors info

  • Mezhlum A. Sumbatyan

    д-р физ.-мат. наук, профессор, главный научный сотрудник Южного федерального университета, профессор кафедры теоретической и компьютерной гидроаэродинамики Института математики, механики и компьютерных наук им. Воровича И.И.

  • Michael Yu. Remizov

    канд. физ.-мат. наук, доцент, старший научный сотрудник Института математики, механики и компьютерных наук им. Воровича И.И. Южного федерального университета

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Issue

Vol. 15 (2018) No. 4

Pages

40-53

Section

Mechanics

Dates

Submitted

September 22, 2018

Accepted

October 19, 2018

Published

December 21, 2018

How to Cite

[1]
Sumbatyan, M.A., Remizov, M.Y., On the 3D elastic wave propagation through a cascading system of three doubly-periodic arrays of co-planar cracks. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2018, т. 15, № 4, pp. 40–53. DOI: 10.31429/vestnik-15-4-40-53

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Copyright (c) 2018 Сумбатян М.А., Ремизов М.Ю.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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