Interaction of harmonic waves with a periodic array of inclined cracks

Y. Mikata*, J. D. Achenbach

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Reflection and transmission of a longitudinal wave by a periodic array of inclined two-dimensional cracks has been investigated. By using the Betti-Rayleigh reciprocity relation, a pair of singular integral equations has been derived for the crack-opening displacements. The singular integral equations have been solved by the use of the boundary element method. Reflection and transmission coefficients of zeroth order have been expressed in terms of the crack-opening displacements by an application of the Betti-Rayleigh reciprocity relation. These coefficients have been computed for normal and oblique incidence, for collinear and inclined cracks, and for various values of the wave number. The results for normal incidence on collinear cracks have been compared with earlier results, and excellent agreement has been obtained. The results for oblique wave incidence or inclined cracks show mode conversion, and they display the dependence of the reflection and the transmission coefficients on the frequency of the incident wave.

Original languageEnglish (US)
Pages (from-to)59-72
Number of pages14
JournalWave Motion
Issue number1
StatePublished - Jan 1988

ASJC Scopus subject areas

  • Modeling and Simulation
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Applied Mathematics

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