Propagation of horizontally polarized transverse waves in a solid with a periodic distribution of cracks

J. D. Achenbach*, Z. L. Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


The propagation of time-harmonic waves in a solid containing a periodic distribution of cracks is investigated in a two-dimensional configuration. The cracks are parallel to the x-axis, and their centers are located at positions x = md, y = lh(m, l = 0, ±1, ±2,...). The wave motion is polarized in the z-direction and propagates in the y-direction (normal to the cracks). The theory of Floquet or Bloch waves, together with an appropriate Green's function and the condition of vanishing traction on the crack faces leads to a system of singular integral equations, which provides the basis for the derivation of an exact dispersion equation. Numerical results are presented for the wave number as a function of the frequency. The frequency spectrum shows a pattern of passing and stopping bands. The exact results are compared with the frequency spectrum according to a simplified theory which considers the arrays of collinear cracks in the planes y = lh (l= 0 ±1, ±2,...) as planes of homogeneous transmission and reflection. Good agreement is observed between exact and approximate results.

Original languageEnglish (US)
Pages (from-to)371-379
Number of pages9
JournalWave Motion
Issue number4
StatePublished - Jul 1986

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Physics and Astronomy
  • Computational Mathematics
  • Applied Mathematics


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