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In the context of elastic wave propagation in damaged solids, an analyticalapproach for scattering of antiplane waves by two-dimensional periodic arraysof cracks is developed. Before considering the study of arrays of cracks, thescattering of an antiplane wave by a flat crack is first studied. Then, usingthe representation formula for the scattered displacement by a flat and byconsidering the periodicity condition of the crack-spacing, a boundary integralequation is obtained for the crack face displacement of the reference crack.Numerical results for the reflection and transmission coefficients arepresented as functions of the crack-spacing, the frequency of excitation, andthe angle of incidence. Finally, the propagation of antiplane waves bytwo-dimensional periodic arrays of cracks is studied. Despite the use of afinite number of linear arrays, one recognizes the effects of band-passfiltering or band rejection characteristics of the transmission spectra of aperiodic medium. Effects due to a disorder in the periodicity are alsoanalysed.

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