Effective wavenumbers and reflection coefficients for an elastic medium containing random configurations of cylindrical scatterers

Abramowitz, 1974 Aguiar, 2000, Antiplane coherent scattering from a slab containing a random distribution of cavities, Proc. Roy. Soc. A, 456, 2883, 10.1098/rspa.2000.0645 Aristégui, 2002, New results for isotropic point scatterers: foldy revisited, Wave Motion, 36, 383, 10.1016/S0165-2125(02)00031-8 Aristégui, 2007, Effective material properties for shear-horizontal acoustic waves in fiber composites, Phys. Rev. E, 75, 056607, 10.1103/PhysRevE.75.056607 Bussink, 1995, Self-consistent analysis of elastic wave propagation in two dimensional matrix-inclusion composites, J. Mech. Phys. Solids, 43, 1673, 10.1016/0022-5096(95)00048-N Chaix, 2006, Ultrasonic wave propagation in heterogeneous solid media: theoretical analysis and experimental validation, Ultrasonics, 44, 200, 10.1016/j.ultras.2005.11.002 Charalambopoulos, 1992, Characterization of functions as radiation patterns in linear elasticity, Math. Meth. Appl. Sci., 15, 547, 10.1002/mma.1670150804 Derode, 2006, Influence of correlations between scatterers on the attenuation of the coherent wave in a random medium, Phys. Rev. E, 74, 036606, 10.1103/PhysRevE.74.036606 Devaney, 1980, Multiple scattering for discrete, elastic random media, J. Acoust. Soc. Am., 21, 2603 Fikioris, 1964, Multiple scattering of waves. II. Hole corrections in the scalar case, J. Math. Phys., 5, 1413, 10.1063/1.1704077 Foldy, 1945, The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers, Phys. Rev., 67, 107, 10.1103/PhysRev.67.107 Hashin, 1964, The elastic moduli of fiber-reinforced materials, J. Appl. Mech. ASME, 31, 223, 10.1115/1.3629590 Kanaun, 2004, Propagation of elastic waves in composites with random set of spherical inclusions (effective medium approach), Wave Motion, 40, 69, 10.1016/j.wavemoti.2003.12.013 Karal, 1964, Elastic electromagnetic and other waves in random medium, J. Math. Phys., 5, 537, 10.1063/1.1704145 Kim, 1995, Dispersion of elastic waves in random particulate composites, J. Acoust. Soc. Am., 97, 1380, 10.1121/1.412080 Lax, 1952, Multiple scattering of waves. II. The effective field in dense systems, Phys. Rev., 85, 621, 10.1103/PhysRev.85.621 Le Bas, 2005, Reflection and transmission by randomly spaced elastic cylinders in a fluid slab-like region, J. Acoust. Soc. Am., 117, 1088, 10.1121/1.1848174 Linton, 2005, Multiple scattering by random configurations of circular cylinders: second-order corrections for the effective wavenumber, J. Acoust. Soc. Am., 117, 3413, 10.1121/1.1904270 Linton, 2006, Multiple scattering by multiple spheres: a new proof of the lloyd-berry formula for the effective wavenumber, SIAM J. Appl. Math., 66, 1649, 10.1137/050636401 Lloyd, 1967, Wave propagation through an assembly of spheres. iv. Relation between different scattering theories, Proc. Phys. Soc. Lond., 91, 678, 10.1088/0370-1328/91/3/321 P.A. Martin, Multiple Scattering: Interaction of Time-harmonic Waves with N Obstacles, Cambridge, New York, 2006. Martin, 2008, Multiple scattering by random configurations of circular cylinders: weak scattering without closure assumptions, Wave Motion, 45, 865, 10.1016/j.wavemoti.2008.03.004 Muller, 1955, Radiation patterns and radiation fields, J. Rat. Mech. Anal., 4, 235 Parnell, 2008, Homogenization for wave propagation in periodic-reinforced media with complex microstructure. I-Theory, J. Mech. Phys. Solids, 56, 2521, 10.1016/j.jmps.2008.02.003 Robert, 2007, Reflection and transmission process from a slab-like region containing a random distribution of cylindrical scatterers in an elastic matrix, Acta Acust Unit Acust, 93, 1 Sabina, 1988, A simple self-consistent analysis of wave propagation in particulate composites, Wave Motion, 10, 127, 10.1016/0165-2125(88)90038-8 Stanke, 1983, A unified theory for elastic wave propagation in polycrystalline materials, J. Acoust. Soc. Am., 75, 665 Tsang, 2001 Twersky, 1962, On scattering of waves by random distributions. I. Free scatterers formalism, J. Math. Phys., 3, 700, 10.1063/1.1724272 Varadan, 1986, Multiple scattering of compressional and shear waves by fiber-reinforced composite materials, J. Acoust. Soc. Am., 80, 333, 10.1121/1.394151 Varadan, 1980 Veksler, 1999, Elastic wave scattering by a cylindrical shell, Wave Motion, 10.1016/S0165-2125(98)00043-2 Waterman, 1961, Multiple scattering of waves, J. Math. Phys., 2, 512, 10.1063/1.1703737 Yang, 1994, Multiple scattering of elastic waves in a fiber-reinforced composite, J. Mech. Phys. Solids, 42, 1945, 10.1016/0022-5096(94)90020-5