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

Abstract

-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.

Axisymmetric scattering of a fluid spheroid illuminated by an acoustical Bessel beam

“…The ideal fluid surrounding the spheroid has an acoustical velocity and a density . The incident pressure field could be expressed as a PWSE as [10,11]:…”

Numerical investigation of the acoustic scattering problem from penetrable prolate spheroidal structures using the Vekua transformation and arbitrary precision arithmetic

“…In the recent years, many studies have been conducted on the acoustic waves (or beams) scattering from elastic, penetrable, and impenetrable spheroids avoiding the use of spheroidal wave functions . The T‐matrix method and partial wave (also known as normal mode or multipole) series expansion method abbreviated PWSE have been used extensively to study Bessel beams scattering from spheroidal obstacles . Bessel beams posses the characteristics of nondiffraction and the ability to retain its form without blocking, which can be advantageous over the plane waves in specific cases.…”

“…[20][21][22][23] The T-matrix method and partial wave (also known as normal mode or multipole) series expansion method abbreviated PWSE have been used extensively to study Bessel beams scattering from spheroidal obstacles. [22][23][24][25][26][27][28] Bessel beams posses the characteristics of nondiffraction and the ability to retain its form without blocking, which can be advantageous over the plane waves in specific cases.…”

Electromagnetic binding and radiation force reversal on a pair of electrically conducting cylinders of arbitrary geometrical cross-section with smooth and corrugated surfaces

“…The formalism is applicable to any range of frequencies such that either the long-or short-wavelength with respect to the size of the particles can be examined rigorously. Notice also that apart from their practical importance, two-dimensional EM scattering and radiation force analytical models provide rigorous, convenient and efficient ways of displaying emergent physical phenomena without involving the mathematical/algebraic manipulations encountered in solving three-dimensional problems [23][24][25][26][27][28][29], and this work could assist in developing numerical codes for arbitrary shaped particles in 3D. *Electronic mail: F.G.Mitri@ieee.org…”