On the oblique penetration of elastic waves into a finite number of equally spaced periodic arrays of obstacles

In the context of wave propagation through damaged elastic solids, an analytical method is developed to study oblique penetration of both longitudinal and transverse plane waves into a doubly periodic array of slit-type obstacles. Reduced the problem to a system of integral equations and then to an algebraic linear system, suitable assumptions on the physical and geometrical parameters allow analytical solution and thus explicit representations for the (zeroth-order) scattering parameters. Several figures are given to reflect the wave properties of the structure.