Ultrasonic backscattering enhancements for obliquely tilted cylinders in water: Steel shells and plastic cylinders

High frequency backscattering enhancements from cylindrical objects in water at large tilt angles are investigated. For steel, leaky waves which travel along the surface of solid cylindrical bars or shells make the most important contributions. In particular, steel cylindrical shells support a flexural wave at sufficiently high frequencies whose properties are analogous to those of the lowest order antisymmetric (a₀) Lamb wave on plates. When the shell is in water and the frequency exceeds the coincidence frequency, that flexural wave becomes leaky and is the major contributor to the scattering by tilted shells. When the tilt angle is equal to the leaky wave coupling angle, leaky rays are launched which run along the meridian of the cylinder and lead to strong backscattering enhancements. At smaller tilt angles, leaky rays may also be launched which follow helical paths on the cylinder. The helical contribution can also be significant and is the focus of this work. However, the ray analysis for the meridional contribution does not apply to the case of helical rays. Thus, it was necessary to develop a separate ray model for helical rays, which was tested against an exact partial wave series (PWS) solution for the case of specular scattering from infinitely long empty cylindrical shells, yielding good agreement. The agreement was obtained for a wide range of tilt angles by allowing for the interference between the meridional and helical contributions and by including a weak anisotropy of the flexural wave parameters in the ray theory. A ray theory was also developed for the case of finite cylindrical shells and compared with the results of experiments with air-filled and water-filled cylindrical shell targets in the frequency range ka = 20–30. The ray theory predicts the general magnitude of the backscattering contributions except for the air-filled shells at the higher frequencies investigated (ka of about 30). This is probably due to an additional loss of energy of leaky waves from their reflection at the cylinder truncation. For more penetrable materials, such as plastics and rubbers, bulk waves transmitted into the interior of solid cylinders give the dominant scattering effects. At a certain critical tilt angle, a backscattering enhancement is observed due to the merging of caustics associated with bulk rays called the caustic merging transition (CMT). This effect is analogous to the merging of rainbow caustics seen in the scattering of light by transparent fibers. The effect only occurs when the refractive index of the cylinder corresponding to the relevant bulk wave (shear or longitudinal) is greater than one. A ray theory was also developed to model this backscattering mechanism. It employs the idea of the Bravais effective refractive index, the effective index of the cylinder for the ray projections onto the base plane of the cylinder. The critical tilt angle for the CMT effect corresponds to an effective refractive index of two. There was found to be general agreement between theory and experiment down to relatively low ultrasonic frequencies (ka as small as 10).