Scattering from an elastic shell and a rough fluid–elastic interface: Theory

Abstract

A null-field T-matrix formalism is developed for scattering a pressure wave from a stationary elastic shell immersed in a homogeneous and isotropic fluid half-space and in proximity to a rough fluid–elastic interface. Helmholtz–Kirchhoff integral representations of the various scattered pressure and displacement fields are constructed. The surface fields are required to satisfy the elastic tensor boundary conditions and the scattered fields are required to satisfy the extended boundary condition. Spherical basis functions are used to construct a free-field T-matrix for the elastic shell and rectangular vector basis functions are used to construct a representation of the free-field T- matrix for the rough fluid–elastic interface. The free-field T-matrices are introduced into the Helmholtz–Kirchhoff and the null-field equations for the shell-interface system and a general system of equations for the spectral amplitudes of the various fields is obtained. The general system of equations is specialized to scattering from periodic surface roughness and an exact solution for the scattered pressure field in the fluid is obtained. Then the general system of equations is specialized to scattering from small-amplitude arbitrary roughness profiles and a perturbative solution is obtained. It is shown that the formalism contains multiple scattering effects on the rough surface and between the rough surface and the shell.

Scattering from rigid and soft targets near a planar boundary: Numerical results

“…However, in the following, the factor e Ϫit and explicit dependence on time are omitted. In this paper, the incident field is a plane wave with wave number k p (1) , polar angle (i) , and azimuthal angle (i) .…”

“…1 specialized to scattering from a planar interface is briefly summarized and notation for discussion of the numerical results is introduced. It is assumed that a stationary source and target are immersed in a homogeneous, isotropic, inviscid, and semi-infinite fluid half-space that is bounded below by the surface of a semi-infinite sediment half-space located a distance d (2) below the center of the target.…”

“…It is assumed that a stationary source and target are immersed in a homogeneous, isotropic, inviscid, and semi-infinite fluid half-space that is bounded below by the surface of a semi-infinite sediment half-space located a distance d (2) below the center of the target. The volume exterior to the target and above the sediment is denoted v (1) , and v (2) is the volume within the sediment. The surfaces s (2) and s (3) are, respectively, the surfaces of the sediment and the target.…”

Diffraction of sound by a poroelastic cylindrical absorber near an impedance plane

“…In a series of papers, Gaunaurd and Huang [19][20][21] employed translational addition theorems for spherical wave functions to study acoustic scattering by a hard spherical body near a hard flat boundary, by a thin spherical shell near a free surface and by an ideal air bubble near the sea surface. Bishop and Smith [22] developed a null-field T-matrix formalism to investigate plane-wave scattering from an elastic spherical shell near a sediment boundary with an arbitrary roughness profile. To gain an understanding of the target-ground interaction affects, Dassios and Kleinman [23] develop a theory for lowfrequency scattering of 3D targets above a flat plane.…”

Comment on “Multiple scattering in a reflecting cavity: Application to fish counting in a tank” [J. Acoust. Soc. Am. 109, 2587–2597 (2001)] (L)

“…(1) and (2) are not applicable to the present case. There is a rich body of literature on acoustic scattering by bodies in the presence of boundaries (e. g. [3][4][5][6]). Correlated scatterers can give rise to interference between multiply scattered waves that is absent in a group of independent scatterers.…”