Abstract
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.
Highlights
The acoustic field in solids presents a complex interference pattern because the compressional wave and the shear wave have different propagation velocities which both have effects on particle velocity, the usual energy method is more accurate than the potential function approach in describing the physical properties of acoustic fields
The vector Helmholtz equation ∇2s + k2s = 0 is introduced in order to obtain the analytical solution of the scattered acoustic field, where s is the displacement vector in solids and it can be decomposed into the following form by field theory: s = L + M + N, (1)
It is difficult to establish the connection between the energy propagation direction and the physical quantities of the acoustic field
Summary
The acoustic field in solids presents a complex interference pattern because the compressional wave and the shear wave have different propagation velocities which both have effects on particle velocity, the usual energy method is more accurate than the potential function approach in describing the physical properties of acoustic fields. Time averaged Umov-Poynting vector is defined as acoustic intensity by Ainslie and Burns [7] when discussing the energy of reflected wave and transmitted wave at the interface of solid. This paper presents a time-space average method by which the physical image and the properties of acoustic energy propagation in the solid are accurately described. The elastic scattering energy of a spherical shell in sandy sediment especially is analyzed using this method
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