Reflection and Transmission by a Periodic Array of Coplanar Cracks: Normal and Oblique Incidence

Abstract

Scattering of in-plane elastic waves by a periodic array of coplanar cracks is investigated. This problem was first treated by Angel and Achenbach. The method of their solution was based on the Fourier series expansion of the Green-Lame potentials. In this paper, we have extended van der Hijden and Neerhoff’s treatment of scattering of in-plane elastic waves by a single crack to the periodic case. Major advantages of our treatment over Angel and Achenbach are: (1) the formulation is relatively simple, straightforward, and unified for both normal and oblique incidence, and (2) more importantly, there is no need for numerical integrations, because all the integrations involved in the formulation can be analytically evaluated thanks to the periodicity of the problem and the coplanarity of the cracks. Numerical results are presented and compared with those of Angel and Achenbach. Some new numerical results are also presented.