Acoustic Response of a Layer of Spherical Inclusions with a Random or Periodic Arrangement

Starting with the classic work of Ying and Truell [1], the scattering of a plane elastic wave by an isolated elastic sphere embedded in an unbounded medium has been studied in great detail. Similarly, the propagation of an effective elastic wave in an elastic matrix containing a random or periodic distribution of inclusions has received considerable attention. By comparison, an intermediate level of microstructure — a single layer of inclusions in an elastic matrix — has received very little attention. Apart from the fact that this problem is worth studying in its own right because of its inherent value as a canonical problem in elastodynamics of materials with a microstructure, it has applications in geophysics and quantitative nondestructive evaluation