An application of the spheroidal-coordinate-based transition matrix: Acoustic scattering from high aspect ratio solids

Abstract

In a previous paper [R. H. Hackman, J. Acoust. Soc. Am. 75, 35–45 (1984)] a spheroidal-coordinate-based transition matrix formalism was established for acoustic and elastic wave scattering. In this paper, we consider the acoustic scattering by a solid elastic cylinder with hemispherical endcaps and a length-to-diameter ratio of 10. Numerical results are presented for the backscattered form function as a function of frequency for various angles of incidence. These results are compared with experimental measurements taken at the Naval Coastal Systems Center and given a physical interpretation.

Acoustic scattering by axisymmetric finite-length bodies with application to fish : measurement and modeling

“…These formally exact, numerically solved methods include the perturbation method (Ogilvy, 1991) which is limited to shapes that are close to a separable geometry, the T-matrix method (Waterman, 1968;Varadan et ai., 1982;Lakhtakia et ai., 1984;Hackman and Todoroff, 1985) and solving the boundary integral equation by the boundary element method (Tobocman, 1984;Francis, 1993) These numerical models are limited in that they can be computationally intensive and numerically unstable as the frequency or irregularity of the surface increases.…”

“…Numerical solutions have also been developed, including the boundary element method (Tobacman, 1984;Francis, 1993), T-matrix (Waterman, 1968;Varadan et al, 1982;Lakhtakia et al, 1984, Hackman andTodoroff, 1985) and the mode matching methods (Yamashita, 1990) All of these approaches are limited in one or more of the following: frequency range, class of surfaces, types of boundary conditions, eccentricity of shape and/or computational implementation and numerical effciency. DiPerna and Stanton (1994) The FMM proved to be accurate over a wide range of frequencies, shapes of cross section, and penetrable (fluid) as well as impenetrable boundary conditions.…”

Sound scattering by cylinders of noncircular cross section

“…There has been extensive research done on this classic problem (for example see [1,2,3] ). This section will give a brief overview of Lhe existing methods that deal with the problem stated above, along with their regions of applicability and shortcomings.…”

“…Another numerical technique is the extended boundary condition or T-Matrix method [27,3,28,13,29]. This method assumes an expansion of the surface fields in terms of a complete set of orthogonal functions, and then uses the Helmholtz integral formula to assure that the Helmholtz equation is satisfied .…”

Acoustic Scattering by Axisymmetric Finite-Length Bodies: An Extension of a 2-Dimensional Conformal Mapping Method

“…Numerical solutions have also been developed, including the boundary element method (Tobacman, 1984;Francis, 1993), T-matrix (Waterman, 1968;Varadan et aL, 1982;Lakhtakia et aL, 1984;Hackman and Todoroff, 1985) and the mode matching methods (Yamashita, 1990). All of these approaches are limited in one or more of the following: frequency range, class of surfaces, types of boundary conditions, eccentricity of shape and/or computational implementation and numerical efficiency.…”