Reflection and transmission of an antiplane shear wave by an infinite array of randomly oriented cracks in an isotropic elastic medium are investigated. The problem has been formulated for an averaged scattered field, and a “periodization” technique has been developed to derive the governing singular integral equation for the conditionally averaged crack-opening displacement. The singular integral equation has been solved by splitting the kernel into a singular and a regular part. A point scatterer approximation was introduced for the part containing the regular kernel. The approximation has been checked by comparison with exact results for a deterministic periodic system. By using this approximation, the coherent part of the averaged reflection and transmission coefficients of zeroth order has been calculated for normal incidence, a completely random crack orientation, and various values of the wavenumber and the ratio of crack length and crack-center spacing. The problem was formulated in the context of antiplane shear waves. The results are, however, also applicable to reflection and transmission of acoustic or electromagnetic waves by an array of screens.PACS numbers: 43.20.Fn, 43.20.Bi.
ASJC Scopus subject areas
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics