On 3D theory of acoustic metamaterials with a triple-periodic system of interior obstacles

  • M. A. SumbatyanEmail author
  • M. Y. Remizov
Original Article


The paper is devoted to a semi-analytical method, to develop analytical expressions for the wave field and the scattering parameters—the reflection and transmission coefficients, when a longitudinal plane wave falls on the system of a finite number of identical doubly periodic gratings parallel to each other, each of them consisting of a periodic array of rectangular cracks in the elastic isotropic medium. In the one-mode frequency range, the problem is reduced to a system of hypersingular integral equations whose solution gives the physical parameters as well as an explicit representation of the wave field inside the structure. The present work continues to study the 3-D problem for arbitrary finite number of such plane arrays which form a triple-periodic system of cracks. The principal aim is to generalize the results obtained previously for elastic 2-D and 3-D problems. Some presented diagrams emphasize new physical properties of the cascading structure.


Triple-periodic array of cracks One-mode regime Hypersingular integral equations Semi-analytical method Reflection and transmission coefficients Acoustic filters 


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The first author is thankful to the Russian Science Foundation (RSCF) for the support by Project 15-19-10008-P.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

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

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