0
Research Papers

The Scattering of Acoustic Wave by a Chain of Elastic Spheres in Liquid

[+] Author and Article Information
Yanru Zhang

Department of Applied Mathematics,
University of Science and Technology Beijing,
Beijing 100083, China
e-mail: zyru1989@163.com

Peijun Wei

Department of Applied Mathematics,
University of Science and Technology Beijing,
Beijing 100083, China
e-mail: weipj@ustb.edu.cn

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 23, 2013; final manuscript received December 17, 2013; published online February 5, 2014. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 136(2), 021023 (Feb 05, 2014) (7 pages) Paper No: VIB-13-1127; doi: 10.1115/1.4026434 History: Received April 23, 2013; Revised December 17, 2013

The scattering of acoustic waves by a chain of elastic spheres in liquid is studied. The incident wave, the scattering wave in the host, and the transmitted waves (including longitudinal and transverse wave modes) in the elastic spheres are all expanded in the form of a series of spherical wave functions. The total waves are obtained by the addition of all scattered waves from individual elastic sphere. The addition theorem of spherical wave function is used to perform the coordinates transform for the scattering waves from different spheres. The expansion coefficients of scattering waves are determined by the interface condition between the elastic spheres and the liquid host. The scattering cross section and the scattering amplitude in far field are computed as numerical examples. Two cases, steel spheres and lead spheres embedded in water, are considered in the numerical examples.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Wolf, A., 1945, “Motion of a Rigid Sphere in an Acoustic Wave Field,” J. Geophys., 10, pp. 91–109. [CrossRef]
Nagase, M., 1957, “Diffraction of Elastic Wave by a Spherical Surface,” J. Phys. Soc. Jpn., 11, pp. 279–301. [CrossRef]
Knopoff, L., 1959, “Scattering of Compressional Waves by Spherical Obstacles,” J. Geophys., 24, pp. 30–39. [CrossRef]
Ying, C. F., and Truell, R., 1956, “Scattering of Plane Longitudinal Wave by Sphercal Obstacle in an Isotropically Elastic Solid,” J. Appl. Phys., 27, pp. 1086–1097. [CrossRef]
Einspruch, N. G., Witterholt, E. J., and Truell, R., 1960, “Scattering of a Plane Transverse Wave by a Sphere Obstacle in an Elastic Medium,” J. Appl. Phys., 31, pp. 806–818. [CrossRef]
Burning, J., and Lo, Y. T., 1969, “Multiple Scattering by Spheres,” Antenna Laboratory, University of Illinois, Urbana, IL, Technical Report No. 69-5.
Burning, J., and Lo, Y. T., 1971, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solutions,” IEEE Trans. Antennas Propag.19(3), pp. 378–390. [CrossRef]
Burning, J., and Lo, Y. T., 1971, “Multiple Scattering of EM Waves by Spheres Part II—Numerical and Experimental Results,” IEEE Trans. Antennas Propag.19(3), pp. 391–400. [CrossRef]
Ivanov, E., 1970, “Diffraction of Electromagnetic Waves by Two Bodies, Nauka i Tekbnika, Minsk, 1968, NASA Technical Translation F-597.
Peterson, B., and Ström, S., 1974, “Matrix Formulation of Acoustic Scattering From an Arbitrary Number of Scatterers,” J. Acoust. Soc. Am., 56(3), pp. 771–778. [CrossRef]
Peterson, B., and Ström, S., 1975, “Matrix Formulation of Acoustic Scattering From Multilayered Scatterers,” J. Acoust. Soc. Am., 57(1), pp. 2–13. [CrossRef]
Gaunaurd, G. C., Huang, H., and Strifors, H. C., 1995, “Acoustic Scattering by a Pair of Spheres,” J. Acoust. Soc. Am., 98(1), pp. 494–507. [CrossRef]
Gaunaurd, G. C., Huang, H., and Strifors, H. C., 1997, “Acoustic Scattering by a Pair of Spheres: Addenda and Corrigenda,” J. Acoust. Soc. Am., 107(5), pp. 2983–2985. [CrossRef]
Gaunaurd, G. C., and Huang, H., 1996, “Sound Scattering by a Spherical Object Near a Hard Flat Bottom,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 43(4), pp. 690–700. [CrossRef]
Gaunaurd, G. C., and Huang, H., 1995, “Acoustic Scattering of a Plane Wave by Two Spherical Elastic Shells,” J. Acoust. Soc. Am., 98(4), pp. 2149–2156. [CrossRef]
Gaunaurd, G. C., and Huang, H., 1997, “Scattering of a Plane Acoustic Wave by a Spherical Elastic Shell Near a Free Surface,” J. Solids Struct., 34(5), pp. 591–602. [CrossRef]
Huang, H., and Gaunaurd, G. C., 1997, “Acoustic Scattering of a Plane Wave by Two Spherical Elastic Shells Above the Coincidence Frequency,” J. Acoust. Soc. Am., 101(5), pp. 2659–2668. [CrossRef]
Gumerov, N. A., and Duraiswami, R., 2002, “Computation of Scattering From N Spheres Using Multipole Reexpansion,” J. Acoust. Soc. Am., 112(6), pp. 2688–2701. [CrossRef] [PubMed]
Fang, X. Q., Hu, C., and Huang, W. H., 2007, “Scattering of Elastic Waves and Dynamic Stress in Two-Particle Reinforced Composite System,” Mech. Mater., 39, pp. 538–547. [CrossRef]
Xu, Y. L., 1998,“Efficient Evaluation of Vector Translation Coefficients in Multi-Particle Light-Scattering Theories,” J. Comput. Phys., 139, pp. 137–165. [CrossRef]
Gumerov, N. A., and Duraiswami, R., 2007, “A Scalar Potential Formulation and Translation Theory for the Time-Harmonic Maxwell Equations,” J. Comput. Phys., 225(1), pp. 206–236. [CrossRef]
Kerr, F. H., 1992, “The Scattering of a Plane Elastic Wave by Spherical Inclusion,” Int. J. Eng. Sci., 30(2), pp. 169–186. [CrossRef]
Xu, Y. L., 1996, “Calculation of the Addition Coefficients in Electromagnetic Multisphere- Scattering Theory,” J. Comput. Phys., 127, pp. 285–298. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The scattering of a chain of elastic spheres under an incident plane longitudinal wave

Grahic Jump Location
Fig. 2

The scattering cross section for steel sphere in water (D = d/a). (a) D = 2; (b) D = 3; (c) D = 4.

Grahic Jump Location
Fig. 3

The scattering cross section for lead sphere in water (D = d/a). (a) D = 2; (b) D = 3; (c) D = 4.

Grahic Jump Location
Fig. 4

The far-field amplitude for steel sphere in water (ka = α0a). (a) ka = 1; (b) ka = 2; (c) ka = 3; (d) ka = 7.5.

Grahic Jump Location
Fig. 5

The far-field amplitude for lead sphere in water (ka = α0a)

Grahic Jump Location
Fig. 6

The comparison of computation accuracy for different term numbers retained (a) D = 2 (b) D = 6

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In