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

Hackman, Roger H.; Todoroff, Douglas G.

doi:10.1121/1.393024

Cited by 24 publications

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“…(15) and (18), that performing the integrals over the surface of the scatterer, to determine individual elements of the Q and ReQ matrices, requires evaluations of n(r, h, /) Á !w. In spherical coordinates, r @=@r ð Þe r þ r À1 @=@h ð Þe h þ r sin h ð Þ À1 @=@/ ð Þe / .…”

Section: Evaluating the T-matrix Elementsmentioning

confidence: 99%

Superspheroidal modeling of resonance scattering from elongated air bubbles and fish swim bladders

Feuillade

2012

The Journal of the Acoustical Society of America

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The extended boundary condition technique of Waterman [J. Acoust. Soc. Am. 45, 1417-1429 (1969)] has been used to make accurate studies of the frequency and azimuthal scattering distributions from extended axisymmetric acoustic objects. These objects are formed using the mathematical function for a "superellipse" [i.e., (x/a)(s) + z/b)(s) = 1, where s = 2n, n = 1,2,[ellipsis (horizontal)]], and revolving around the z-axis. For s = 2, the object is a spheroid with aspect ratio α = b/a. As s increases, the shape of the object approaches a right circular cylinder of diameter 2a and length 2b. The method is applied to the case of prolate (i.e., α > 1) air-filled objects in water, which has importance for the interpretation of acoustic scattering from oceanic objects such as air-bubbles, the swim bladders of some fish, and zooplankton. It is found that the resonance frequency increases with α, essentially as predicted using a different method by Weston, and increases in a relatively minor way with s. The resonance peak amplitude, and Q, are also more sensitive to changes in α, than s. The method shows that the monopole resonance continues to dominate low frequency scattering, leading to an almost spherically symmetric azimuthal scattering distribution, even for elongated, cylindrical, air-filled, objects with an aspect ratio up to α = 20, and s = 32.

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Section: Evaluating the T-matrix Elementsmentioning

confidence: 99%

Superspheroidal modeling of resonance scattering from elongated air bubbles and fish swim bladders

Feuillade

2012

The Journal of the Acoustical Society of America

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“…Although various works examined the acoustic scattering by a spheroid using the separation of variables method in spheroidal coordinates [20][21][22][23][24], other analyses have investigated the T-matrix (or null-field) method [4,5,[25][26][27][28][29] the finite element method (FEM) [30], the finite difference [2] time-domain method [31], the fast multipole [32] accelerated boundary element method (BEM) [33], the 3D-BEM [34], the B Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric scattering of an acoustical bessel beam by a rigid fixed spheroid

Mitri

2015

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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-Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure ( = ) in the near-field and the backscattering form function in the far-field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam , and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) due to the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the nearand far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.

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Probe model implementation in the null field approach to crack scattering

Wirdelius¹

1992

J Nondestruct Eval

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

Cited by 24 publications

References 0 publications

Superspheroidal modeling of resonance scattering from elongated air bubbles and fish swim bladders

Superspheroidal modeling of resonance scattering from elongated air bubbles and fish swim bladders

Axisymmetric scattering of an acoustical bessel beam by a rigid fixed spheroid

Probe model implementation in the null field approach to crack scattering

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