Acoustic scattering from phononic crystals with complex geometry.

This work introduces a formalism for computing external acoustic scattering from phononic crystals (PCs) with arbitrary exterior shape using a Bloch wave expansion technique coupled with the Helmholtz-Kirchhoff integral (HKI). Similar to a Kirchhoff approximation, a geometrically complex PC's surface is broken into a set of facets in which the scattering from each facet is calculated as if it was a semi-infinite plane interface in the short wavelength limit. When excited by incident radiation, these facets introduce wave modes into the interior of the PC.

A three-dimensional Bloch wave expansion to determine external scattering from finite phononic crystals.

External scattering from a finite phononic crystal (PC) is studied using the Helmholtz-Kirchhoff integral theorem integrated with a Bloch wave expansion (BWE). The BWE technique is used to describe the internal pressure field of a semi-infinite or layered PC subject to an incident monochromatic plane wave. Following the BWE solution, the Helmholtz-Kirchhoff integral is used to determine the external scattered field.

Bloch-wave expansion technique for predicting wave reflection and transmission in two-dimensional phononic crystals.

In this paper acoustic wave reflection and transmission are studied at the interface between a phononic crystal (PC) and a homogeneous medium using a Bloch wave expansion technique. A finite element analysis of the PC yields the requisite dispersion relationships and a complete set of Bloch waves, which in turn are employed to expand the transmitted pressure field. A solution for the reflected and transmitted wave fields is then obtained using continuity conditions at the half-space interface.

Computation of acoustic absorption in media composed of packed microtubes exhibiting surface irregularity.

A multi-scale homogenization technique and a finite element-based solution procedure are employed to compute acoustic absorption in smooth and rough packed microtubes. The absorption considered arises from thermo-viscous interactions between the fluid media and the microtube walls. The homogenization technique requires geometric periodicity, which for smooth tubes is invoked using the periodicity of the finite element mesh; for rough microtubes, the periodicity invoked is that associated with the roughness.