Simulation of elastic wave diffraction by multiple strip-like cracks in layered periodic composite

Numerical modeling of the harmonic motion of a layered phononic crystal (elastic periodic composite) with a set of co-planar strip-like cracks and the accompanying wave phenomena are studied. To simulate an incident field, a transfer matrix method is used. This method allows one to calculate wave-fields and to estimate band gaps and localization factor. The wave-field scattered by a set of strip-like cracks is a superposition of the wave-fields scattered by each crack. All the scattered wave-fields have integral representations in the form of convolution of Fourier symbols of Green’s matrix of the corresponding layered structures and the Fourier transform of crack opening displacements. Crack opening displacements are calculated by applying the Bubnov-Galerkin scheme along with the boundary integral equation method. To solve the system of integral equations, Chebyshev polynomials of the second kind are used because they take into account the square root behaviour of crack opening displacement. The system of linear algebraic equations arising after discretization is composed of matrices describing interactions between cracks. Wave characteristics that allow describing wave phenomena related to elastic wave diffraction by a set of cracks are analysed, and corresponding examples are given. Resonance scattering by a system of cracks depending on the defect situation is investigated, the streamlines of wave energy flows are constructed, and the results are discussed.