Abstract
We extend the multiple-scattering theory (MST) to out-of-plane propagating elastic wavesin 2D periodical composites by taking into account the full vector character. The formalismfor both the band structure calculation and the reflection and transmission coefficientcalculation for finite slabs is presented. The latter is based on a double-layer scheme, whichobtains the reflection and transmission matrix elements for the multilayer slab fromthose of a single layer. Being more rapid in both the band structure and thetransmission coefficient calculations for out-of-plane propagating elastic waves, ourapproach especially shows great advantages in handling the systems with mixedsolid and fluid components, for which the conventional plane wave approach fails.As the applications of the formalism, we calculate the band structure as wellas the transmission coefficients through finite slabs for systems with lead rodsin an epoxy host, steel rods in a water host and water rods in a PMMA host.
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