Acoustic Response of a Layer of Spherical Inclusions with a Hexagonal or Square Periodic Arrangement

Starting with the work of Wolf [1], the scattering of a plane elastic wave by an isolated sphere embedded in an unbounded (or bounded) medium has been studied in great detail [2–3]. Similarly, the propagation of an effective elastic wave in an elastic matrix containing a random or periodic distribution of inclusions (particles, voids, cracks, etc.) has received considerable attention. The literature concerning these two problems is so extensive that its review is beyond the scope of this paper. By comparison, an intermediate level of microstructure, an elastic matrix containing a single layer of a random or periodic distribution of inclusions, has received very little attention. Although this problem is worth examining in its own right because of its inherent value as a canonical problem of elastodynamics of materials with microstructure, it also has applications in geophysics, quantitative nondestructive evaluation, and the design of ultrasound absorptive materials