T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps

In this paper, the T-matrix (null-field) method is developed to investigate the acoustic scattering by a rigid fixed (immovable) finite cylinder with two spheroidal endcaps immersed in a non-viscous fluid under the illumination of an unbounded zeroth-order Bessel beam with arbitrary orientation. Based on the proposed method, a MATLAB software package is constructed accordingly, and then verified and validated to compute the acoustic scattering by a rigid finite-length cylinder in the Bessel beam. Several numerical examples are carried out to investigate the novel phenomenon of acoustic scattering by a cylinder with spheroidal endcaps in a Bessel beam with arbitrary incidence, with particular emphasis on the aspect ratios (including the ratio of total length to diameter of the finite cylinder and the ratio of polar radius to equatorial radius of the spheroidal endcaps), the 'half-cone angle of Bessel beam, the dimensionless frequency, as well as the angle of incidence. The quasi periodic oscillations are observed in the plots of the far-field backscattering form function modulus versus the dimensionless frequency, owing to the interference between the specular reflection and the Franz wave circumnavigating the finite cylinder in the surrounding fluid. A geometrical model of Bessel beam scattering is employed to further verify the effectiveness of the T-matrix method. Furthermore, the 3D far-field scattering directivity patterns at end-on incidence and 2D polar plots at arbitrary angles of incidence are exhibited, which could provide new insights into the physical mechanisms of Bessel beam scattering by finite cylinders with spheroidal endcaps of different aspect-ratios. This research work provides an impetus for engineering applications in underwater acoustics, particle characterization and the interaction of elongated structures with acoustical Bessel beams.