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, Российская Федерация
  • Remizov M.Yu. South Federal University, Rostov-on-Don, Российская Федерация

UDC

539.3

DOI:

https://doi.org/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

Acknowledgement

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

Author Infos

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.

e-mail: masumbatyan@sfedu.ru

Michael Yu. Remizov

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

e-mail: remizov72@mail.ru

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Issue

2018. Vol. 15. No. 4

Section

Mechanics

Pages

40-53

Submitted

2018-09-22

Published

2018-12-21

How to Cite

Sumbatyan M.A., Remizov M.Yu. 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, vol. 15, no. 4, pp. 40-53. DOI: https://doi.org/10.31429/vestnik-15-4-40-53 (In Russian)

Copyright (c) 2018 Sumbatyan M.A., Remizov M.Yu.

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