High-frequency acoustic scattering from submerged cylindrical shells coated with viscoelastic absorbing layers

Abstract

We analyze the high-frequency scattering of a plane-wave incident on a submerged air-filled cylindrical steel shell coated with a viscoelastic layer. The scattered pressure field consists of a geometrical acoustic contribution and another part due to creeping waves. We analyze the resulting generalized reflection coefficient as a function of azimuthal angle, for two shell sizes and various viscosity levels of the coating. We also obtain the locations of roots of the 10×10 characteristic determinant in the complex ν-plane for the two shell sizes of interest. These zeroes are compared to the zeroes of rigid and soft cylinders and to the roots of a simpler 3×3 determinant corresponding to the case of a solid sound-absorbing cylinder of the same size. The results show that the region in the ν-plane where many of the roots are usually concentrated for bare structures, contain no roots after the absorbing layer is bonded to the steel shell. All the above information is then used to compare the normal-mode solution for the sonar cross section of the coated cylindrical shell found in an earlier study of ours (and extended here to higher k1c values), and the corresponding expression obtained to lowest order from an application of the Watson–Sommerfeld transformation. This comparison, as exhibited in various graphs, is found to be very favorable. It verifies that the lowest-order term in the Watson–Sommerfeld transformed solution is capable of accurately reproducing the exact scattering solution at high frequencies for the cylindrical coated target considered here.