Study on underwater acoustic scattering is very important for detection, location, and recognition of underwater targets. In the past decades, most investigations in this respect were focused on the case of plane wave incidence. But the Bessel beam is a kind of approximate non-diffracting beam with an excellent directing property, so more attention should be paid on it. So far, according to the literature, the studies about underwater acoustic scattering of a Bessel beam mainly focused on spheres and spherical shells using the partial wave series form. When the scatterers become complex objects, the partial wave series form fails to deal with these kinds of problems. To overcome this shortage, the T-matrix method has been introduced to calculate the underwater scattering of a Bessel beam by complex rigid objects. In this paper, the underwater acoustic scattering of a Bessel beam by rigid objects with arbitrary shapes calculated by T-matrix method is studied. By means of the harmonic expansion of Bessel beam, the expression of the incident coefficient can be derived. Through the transmission matrix that relates the known coefficients of expansion of an incident wave to the unknown expansion coefficients of the scattered field, the acoustic scattering formula of a Bessel beam by a rigid scatterer with arbitrary shape is established. In this paper, the backscattering fields of rigid spheroids and finite cylinders with two spheroidal endcaps are discussed, and the backscattering form function modulus vertical bar F vertical bar is curved as a function of dimensionless frequency ka. Subsequently, the peak to peak intervals in backscattering form function caused by the interference of the specular wave and the Franz wave are also analyzed in geometry. The calculated results show that the frequency interval obtained from the curves agrees well with those obtained by geometric analysis for the rigid objects. Meanwhile, for both the rigid spheroid and finite cylinder, the highlight model is successfully applied to explain the phenomenon in which the amplitude of backscattering form function changes with the cone angle of the Bessel beam. From the above numerical results and analysis, the T-matrix method has been successfully introduced to calculate the acoustic scattering of the Bessel beam by complex objects, which extends the application of the T-matrix method and provides a useful tool to explore the characteristics of the Bessel beam.
