Scattering of antiplane elastic waves by two-dimensional periodic arrays of cracks

Mihai Caleap

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Abstract

In the context of elastic wave propagation in damaged solids, an analytical approach for scattering of antiplane waves by two-dimensional periodic arrays of cracks is developed. Before considering the study of arrays of cracks, the scattering of an antiplane wave by a flat crack is first studied. Then, using the representation formula for the scattered displacement by a flat and by considering the periodicity condition of the crack-spacing, a boundary integral equation is obtained for the crack face displacement of the reference crack. Numerical results for the reflection and transmission coefficients are presented as functions of the crack-spacing, the frequency of excitation, and the angle of incidence. Finally, the propagation of antiplane waves by two-dimensional periodic arrays of cracks is studied. Despite the use of a finite number of linear arrays, one recognizes the effects of band-pass filtering or band rejection characteristics of the transmission spectra of a periodic medium. Effects due to a disorder in the periodicity are also analysed.
Original languageFrench
JournalarXiv
Publication statusPublished - 6 Feb 2013

Bibliographical note

21 pages (including 9 figures), in French

Keywords

  • cond-mat.mtrl-sci
  • math-ph
  • math.MP

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