Propagation of antiplane waves in an elastic solid containing a distribution of parallel cracks
Koba, Yuri Kostyantynovych
Master of Science
The propagation of antiplane waves in an unbounded linearly elastic solid that contains a distribution of flat cracks is considered. The cracks are parallel to each other, the distribution is dilute, and a wave is obliquely incident on the planes of the cracks. It is assumed that the multiple scattering produces a coherent wave that loses energy as it propagates. The attenuation coefficient is specified in terms of the power scattered by a single crack and the number of cracks per unit volume. Using the Kramers-Kronig relations, the speed of the coherent wave in the cracked solid is derived as a function of the frequency and of the crack density. Curves are presented for the attenuation coefficient versus the frequency, and for the speed versus the frequency and the crack density. These curves show that the speed of the coherent wave in a cracked solid is always less than the speed in an uncracked solid.