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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.

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Figures

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Fig. 1

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

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Fig. 3

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

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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.

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Fig. 5

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

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Fig. 6

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

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Fig. 2

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

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