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Mathematical Problems in Engineering
Volume 2017, Article ID 9471581, 7 pages
Research Article

A Study on the Scattering Energy Properties of an Elastic Spherical Shell in Sandy Sediment Using an Improved Energy Method

College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China

Correspondence should be addressed to GuangPing Zhu; moc.kooltuo@0762-5e

Received 23 September 2016; Accepted 22 December 2016; Published 13 February 2017

Academic Editor: Andrea Crivellini

Copyright © 2017 WenKai Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An elastic wave is composed of compressional (longitudinal) waves and shear (transverse) waves which have different wave velocities in solids. The acoustic field presents complex interference patterns which means its phenomena and properties are difficult to reveal. Fortunately, the energy method is more accurate than the potential function approach in describing the physical properties of the acoustic field. However, the polarization state of particle vibration excited by an elastic wave is spatially periodic in the wave propagation direction. Therefore, the energy propagation direction is not consistent with the wave propagation direction using commonly used energy method. According to the polarization state of particle vibration, a time-space averaging method based on the spatial periodicity of energy flux in the solid is proposed. The method could eliminate the influence of the interference due to local energy exchange and retain the trend of energy propagation. Several conclusions are illustrated through the analysis of the scattering energy properties of a steel shell in sandy sediment. Sandy sediment can not be regarded as a fluid nor a general solid. Scattering energy excited by an incident shear wave mainly concentrates in the vicinity of the directions of backscattering and forward scattering. Especially, at low frequency, it plays an important role in the total scattering energy excited by an incident compressional and shear wave.