Interaction of harmonic waves with a periodic array of interface cracks in a multi-layered medium: anti-plane case

Abstract

The interaction of anti-plane elastic waves with a periodic array of interface cracks in a multi-layered medium is analyzed in this paper. The number of the layers is arbitrary and the cracks may be distributed on any one of the interfaces. Transfer matrix and Fourier series techniques are used to formulate the mixed boundary-value problem in terms of a Hilbert singular integral equation. Numerical solutions are presented for some typical cases: (i) two bonded half-spaces, (ii) a layer bonded to a half-space, (iii) two half-spaces bonded through a layer, (iv) two layers bonded to a half-space. The dependence of the dynamic stress intensity factors (DSIFs) on the frequency of the incident wave, and the influences of geometric configuration, material combination and incident angle are discussed in detail. The results show that the DSIF–frequency curves involve sharp dips and peaks in many cases, i.e. the DSIF drops to a very low value or rises to a very high value in a surprisingly narrow region of frequency. We analyze this phenomenon in detail and find that the rapid change of the DSIF in a quite narrow frequency region is caused by particular modes of Love waves propagating in the elastic layers.