Mechanics of Solids

, Volume 53, Issue 3, pp 295–306 | Cite as

One-Mode Propagation of Elastic Waves through a Doubly Periodic Array of Cracks

  • M. Yu. Remizov
  • M. A. SumbatyanEmail author


The article is devoted to the derivation of analytical expressions for the reflection and propagation coefficients, when a plane longitudinal wave falls on a system of a finite number of consecutively located identical flat gratings, each of which consists of a periodic array of rectilinear cracks in an elastic isotropic medium. The problem is solved in a flat statement. In the mode of single-mode frequency range, the problem is reduced to a system of hypersingular integral equations, the solution of which gives the reflection and propagation coefficients, as well as the representation of the wave field inside the medium.


reflection and propagation coefficients doubly periodic lattice hypersingular integral equation crack system acoustic filter 


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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.South Federal UniversityRostov-on-DonRussia

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