In-plane waves in an elastic solid containing a cracked slab region

Abstract

Propagation of longitudinal and transverse waves in an elastic solid that contains a cracked slab region is investigated. The cracks have a uniform probability density in the slab region, are parallel to the boundaries of the slab, and the solid is uncracked on either side of the slab. The waves are normally incident on the cracks. It is shown that the resulting average total motion in the solid is governed by a pair of coupled integral equations. These equations are solved under the special assumption that the average exciting motion near a fixed crack is equal to the average total motion. In this case, one finds that in the cracked region, where multiple scattering occurs, there is a forward motion and a backward motion. The two motions have identical frequency-dependent velocity and attenuation, for which simple closed-form formulae are obtained. Simple formulae are also obtained for the wave amplitudes outside the slab. Numerical results corresponding to the velocity, attenuation, reflection amplitude, and transmission amplitude are presented for several values of crack density and slab thickness.