One-mode wave propagation through a periodic array of inteface cracks: explicit 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 between two different materials. The problem is firstly reduced to a 2x2 system of integral equations holding over the opening between adjacent cracks; then, by applying simple (but uniform) approximations valid in the given regime of propagation, some auxiliary integral equations are deduced which are independent on frequency. A linear system is finally set up whose solution leads to explicit analytical formulas for the relevant scattering parameters. By solving numerically the above equations to calculate some constants, several graphs can be provided which reflect the peculiarities of the structure. Comparison between such formulas and corresponding full-numerical solutions of the originary integral system points out very good agreement.