Scattering of antiplane elastic waves by two-dimensional periodic arrays of cracks

TL;DR

This paper develops an analytical method to study how antiplane elastic waves scatter when passing through two-dimensional periodic arrays of cracks, revealing band-pass filtering effects and the impact of disorder.

Contribution

It introduces a boundary integral equation approach for scattering by periodic crack arrays, including effects of disorder and frequency-dependent transmission characteristics.

Findings

Periodic arrays exhibit band-pass filtering of waves.

Disorder affects wave transmission and scattering.

Numerical results show dependence on crack spacing and incident angle.

Abstract

In the context of elastic wave propagation in damaged solids, an analytical approach for scattering of antiplane waves by two-dimensional periodic arrays of cracks is developed. Before considering the study of arrays of cracks, the scattering of an antiplane wave by a flat crack is first studied. Then, using the representation formula for the scattered displacement by a flat and by considering the periodicity condition of the crack-spacing, a boundary integral equation is obtained for the crack face displacement of the reference crack. Numerical results for the reflection and transmission coefficients are presented as functions of the crack-spacing, the frequency of excitation, and the angle of incidence. Finally, the propagation of antiplane waves by two-dimensional periodic arrays of cracks is studied. Despite the use of a finite number of linear arrays, one recognizes the effects of band-pass filtering or band rejection characteristics of the transmission spectra of a periodic medium. Effects due to a disorder in the periodicity are also analysed.