One-mode wave propagation through a periodic array of interface cracks: Explicit analytical results

In the context of wave propagation in damaged composite elastic media, an analytical approach is developed to study the normal penetration of a longitudinal wave into a periodic array of interface thin defects (cracks) between two different materials. The problem is reduced to some integral equations which hold over the opening between adjacent cracks and are independent on frequency. By means of an original procedure, such equations are solved and some related integrals are calculated, so that an explicit analytical representation can be provided for the relevant scattering parameters. Finally, several graphs are set up which reflect the peculiarities of the structure; an excellent agreement is observed—in the concerned (one-mode) regime of propagation—between the obtained formulas and results from a full-numerical treatment of the problem.