Multiple-scattering theory for out-of-plane propagation of elastic waves in two-dimensional phononic crystals

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

[1]  Chan,et al.  Existence of a photonic gap in periodic dielectric structures. , 1990, Physical review letters.

[2]  E. Yablonovitch,et al.  Photonic band structure: The face-centered-cubic case. , 1989, Physical review letters.

[3]  Eleftherios N. Economou,et al.  Multiple-scattering theory for three-dimensional periodic acoustic composites , 1999 .

[4]  A. Modinos,et al.  Scattering of elastic waves by periodic arrays of spherical bodies , 2000 .

[5]  John H. Page,et al.  Elastic Wave Scattering by Periodic Structures of Spherical Objects: Theory and Experiment , 2000 .

[6]  Petit,et al.  Efficient calculation of the Green's function for electromagnetic scattering by gratings. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Eleftherios N. Economou,et al.  Band structure of elastic waves in two dimensional systems , 1993 .

[8]  Eleftherios N. Economou,et al.  Stop bands for elastic waves in periodic composite materials , 1994 .

[9]  Thibaut Sylvestre,et al.  Phononic band-gap guidance of acoustic modes in photonic crystal fibers , 2005 .

[10]  M. Torres,et al.  ULTRASONIC BAND GAP IN A PERIODIC TWO-DIMENSIONAL COMPOSITE , 1998 .

[11]  C. Goffaux,et al.  Theoretical study of a tunable phononic band gap system , 2001 .

[12]  B. Djafari-Rouhani,et al.  Guided elastic waves along a rod defect of a two-dimensional phononic crystal. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  B. Djafari-Rouhani,et al.  Theory of acoustic band structure of periodic elastic composites. , 1994, Physical review. B, Condensed matter.

[14]  B. Djafari-Rouhani,et al.  Out-of-plane propagation of elastic waves in two-dimensional phononic band-gap materials. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Jing Shi,et al.  Theory for elastic wave scattering by a two-dimensional periodical array of cylinders: An ideal approach for band-structure calculations , 2003 .