Dynamic response of a solid with a cracked slab region

The time-harmonic response of an elastic solid with a cracked slab region is analysed. The slab region is permeated by a random distribution of aligned penny-shaped cracks and the solid is uncracked outside this region. Longitudinal waves propagating along the direction normal to the crack surfaces are considered. In the case of waves with half-wavelength greater than the crack diameter, explicit expressions are given for the attenuation and phase velocity of the mean wave in the cracked region, and for the amplitudes of the reflected and transmitted waves in the uncracked parts of the solid. Numerical examples show the influence of the cracked-slab thickness and of the crack density on the overall dynamic response of the medium.