Multiple scattering by random configurations of circular cylinders: Second-order corrections for the effective wavenumber

Journal of the Acoustical Society of America

Volumn 117, Issue 6, 2005, Pages 3413-3423

  Linton, C M ^a   Martin, P A ^b  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^b Department of Geology and Geological Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CORRELATION METHODS; FUNCTIONS; WAVE EFFECTS;

LAX QUASICRYSTALLINE APPROXIMATION; PAIR-CORRELATION FUNCTION; RANDOM ARRAYS; WAVENUMBERS;

ACOUSTIC WAVE SCATTERING;

ARTICLE; GEOMETRY; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; PRIORITY JOURNAL; SYSTEM ANALYSIS; WAVEFORM;

EID: 20444376913     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.1904270     Document Type: Article

References (37)

1. Aristégui, C., and Angel, Y. C. (2002). "New results for isotropic point scatterers: Foldy revisited," Wave Motion 36, 383-399.
2. Attenborough, K. (2002). "Sound propagation close to the ground," Annu. Rev. Fluid Mech. 34, 51-82.
3. Bose, S. K. (1996). "Ultrasonic plane SH wave reflection from a unidirectional fibrous composite slab," J. Sound Vib. 193, 1069-1078.
4. Bose, S. K., and Mal, A. K. (1973). "Longitudinal shear waves in a fiberreinforced composite," Int. J. Solids Struct. 9, 1075-1085.
5. Bussink, P. G. J., Iske, P. L., Oortwijn, J., and Verbist, G. L. M. M. (1995). "Self-consistent analysis of elastic wave propagation in two-dimensional matrix-inclusion composites," J. Mech. Phys. Solids 43, 1673-1690.
6. Dukhin, A. S., and Goetz, P. J. (2001). "Acoustic and electroacoustic spectroscopy for characterizing concentrated dispersions and emulsions," Adv. Colloid Interface Sci. 92, 73-132.
7. Embleton, T. F. W. (1966). "Scattering by an array of cylinders as a function of surface impedance," J. Acoust. Soc. Am. 40, 667-670.
8. Fikioris, J. G. (1966). "Multiple scattering from inhomogeneous media," IEEE Trans. Antennas Propag. 14, 202-207.
9. Fikioris, J. G., and Waterman, P. C. (1964). "Multiple scattering of waves. II. 'Hole corrections' in the scalar case," J. Math. Phys. 5, 1413-1420.
10. Foldy, L. L. (1945). "The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers," Phys. Rev. 67, 107-119.
11. Gradshteyn, I. S., and Ryzhik, I. M. (2000). Tables of Integrals, Series and Products, 6th ed. (Academic, New York).
12. Groenenboom, J., and Snieder, R. (1995). "Attenuation, dispersion, and anisotropy by multiple scattering of transmitted waves through distributions of scatterers," J. Acoust. Soc. Am. 98, 3482-3492.
13. Hipp, A. K., Storti, G., and Morbidelli, M. (1999). "On multiple-particle effects in the acoustic characterization of colloidal dispersions," J. Phys. D 32, 568-576.
14. Ishimaru, A. (1978). Wave Propagation and Scattering in Random Media (Academic, New York), Vol. 2.
15. Kanaun, S. K. (2000). "Self-consistent methods in the problems of wave propagation through heterogeneous media," Heterogeneous Media. Micromechanics Modeling Methods and Simulations, edited by K. Markov and L. Preziosi (Birkhäuser, Boston), pp. 241-319.
16. Kanaun, S. K., and Levin, V. M. (2003). "Effective medium method in the problem of axial elastic shear wave propagation through fiber composites," Int. J. Solids Struct. 40, 4859-4878.
17. Kim, J.-Y (2003). "Antiplane shear wave propagation in fiber-reinforced composites," J. Acoust. Soc. Am. 113, 2442-2445.
18. Kim, J.-Y., Ih, J.-G., and Lee, B.-H. (1995). "Dispersion of elastic waves in random paniculate composites," J. Acoust. Soc. Am. 97, 1380-1388.
19. Lax, M. (1951). "Multiple scattering of waves," Rev. Mod. Phys. 23, 287-310.
20. Lax, M. (1952). "Multiple scattering of waves. II. The effective field in dense systems," Phys. Rev. 85, 621-629.
21. Linton, C. M., and McIver, P. (2001). Handbook of Mathematical Techniques for Wave/Structure Interactions (Chapman & Hall/CRC, Boca Raton).
22. Lloyd, P., and Berry, M. V. (1967). "Wave propagation through an assembly of spheres IV. Relations between different multiple scattering theories," Proc. Phys. Soc. London 91, 678-688.
23. Mal, A. K., and Knopoff, L. (1967). "Elastic wave velocities in two-component systems," J. Inst. Math. Appl. 3, 376-387.
24. McClements, D. J., Fairley, P., and Povey, M. J. W. (1990). "Comparison of effective medium and multiple-scattering theories of predicting the ultrasonic properties of dispersions," J. Acoust. Soc. Am. 87, 2244-2246.
25. Povey, M. J. W. (1997). Ultrasonic Techniques for Fluids Characterization (Academic, San Diego).
26. Price, M. A., Attenborough, K., and Heap, N. W. (1988). "Sound attenuation through trees: measurements and models," J. Acoust. Soc. Am. 84, 1836-1844.
27. Siqueira, P. R., and Sarabandi, K. (1996). "Method of moments evaluation of the two-dimensional quasi-crystalline approximation," IEEE Trans. Antennas Propag. 44, 1067-1077.
28. Siqueira, P. R., Sarabandi, K., and Ulaby, F. T. (1995). "Numerical simulation of scatterer positions in a very dense medium with an application to the two-dimensional Born approximation," Radio Sci. 30, 1325-1339.
29. Spelt, P. D. M., Norato, M. A., Sangani, A. S., Greenwood, M. S., and Tavlarides, L. L. (2001). "Attenuation of sound in concentrated suspensions: theory and experiments," J. Fluid Mech. 430, 51-86.
30. Tsang, L., Kong, J. A., Ding, K.-H., and Ao, C. O. (2001). Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, New York).
31. Twersky, V. (1962). "On scattering of waves by random distributions. I. Free-space scatterer formalism," J. Math. Phys. 3, 700-715.
32. Twersky, V. (1978). "Acoustic bulk parameters in distributions of pair-correlated scatterers," J. Acoust. Soc. Am. 64, 1710-1719.
33. Varadan, V. K., Ma, Y., and Varadan, V. V. (1986). "Multiple scattering of compressional and shear waves by fiber-reinforced composite materials," J. Acoust. Soc. Am. 80, 333-339.
34. Varadan, V. K., Varadan, V. V., and Pao, Y-H. (1978). "Multiple scattering of elastic waves by cylinders of arbitrary cross section. I. SH waves," J. Acoust. Soc. Am. 63, 1310-1319.
35. Verbis, J. T., Kattis, S. E., Tsinopoulos, S. V., and Polyzos, D. (2001). "Wave dispersion and attenuation in fiber composites," Computational Mech. 27, 244-252.
36. Waterman, P. C., and Truell, R. (1961). "Multiple scattering of waves," J. Math. Phys. 2, 512-537.
37. Yang, R.-B., and Mal, A. K. (1994). "Multiple scattering of elastic waves in a fiber-reinforced composite," J. Mech. Phys. Solids 42, 1945-1968.