Scattering of harmonic elastic anti-plane shear waves by two collinear symmetric cracks in infinite long strip using the non-local theory

The problem of two collinear symmetric cracks in an infinite long strip where the cracks' surfaces are subjected to the harmonic anti-plane shear wave was studied. The field equations of non-local elasticity theory were employed to formulate and solve this problem. A one-dimensional non-local kernel is used to instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress occurs at the crack tips. In solving the equations, the crack surface displacement is expanded in a series using Jacobi's polynomials and Schmidt's method is used.