Search

Scattering of waves as a result of a vertical array of equally spaced cracks on a square lattice is studied. The convenience of Floquet periodicity reduces the study to that of scattering of a specific wave-mode from a single crack in a waveguide. The discrete Green's function, for the waveguide, is used to obtain the semi-analytical solution for the scattering problem in the case of finite cracks whereas the limiting case of semi-infinite cracks is tackled by an application of the Wiener–Hopf technique. Reflectance and transmittance of such an array of cracks, in terms of incident wave parameters, is analysed. Potential applications include construction of tunable atomic-scale interfaces to control energy transmission at different frequencies. [ABSTRACT FROM AUTHOR]

Scattering of time-harmonic plane wave by two parallel semi-infinite rows, but with staggered edges, is considered on square lattice. The condition imposed on the semi-infinite rows is a discrete analogue of Neumann boundary condition. A physical interpretation assuming an out-of-plane displacement for the particles arranged in the form of a square lattice and interacting with nearest neighbours associates the scattering problem with lattice wave scattering due to the presence of two staggered but parallel crack tips. The discrete scattering problem is reduced to the study of a pair of Wiener–Hopf equation on an annulus in complex plane, using Fourier transforms. Due to the offset between the crack edges, the Wiener–Hopf kernel, a 2 × 2 matrix, is not amenable to factorization in a desirable form and an asymptotic method is adapted. Further, an approximation in the far field is carried out using the stationary phase method. A graphical comparison between the far-field approximation based on asymptotic Wiener–Hopf method and that obtained by a numerical solution is provided. Also included is a graphical illustration of the low-frequency approximation, where it has been found that the numerical solution of the scattering problem coincides with the well-known formidable solution in the continuum framework. [ABSTRACT FROM AUTHOR]