Guided interfacial waves at a periodic array of coplanar disbonds in a solid

Abstract

This paper is concerned with guided elastic waves at a periodic array of coplanar disbonds in a solid, and the role they play in the scattering of bulk waves. It is approached as a mixed boundary condition problem pertaining to two elastic half spaces which are joined together within infinitely long regularly spaced strips, and unattached in between. It provides an approach to modeling wave interactions at an array of coplanar cracks, solids with slightly uneven surfaces which are in contact, stoping in mine operations where a narrow seam of a mineral is removed leaving regularly positioned pillars for roof support, and other analogous physical situations. In the analysis, a truncated Fourier series representation of the wave field is invoked, and the boundary conditions are applied at a discrete set of points within the repeat interval at the interface to determine the Fourier coefficients. The dispersion relation for interfacial waves is obtained within a one dimensional folded Brillouin zone scheme, and it is shown that there are branches associated with leaky interfacial waves, which at certain isolated points in wavevector space uncouple from the bulk wave continuum to exist as secluded supersonic interfacial waves. These observations are able to explain striking resonant features in the scattering of bulk waves at the interface.