H. Huang
Naval Surface Warfare Center, Indian Head Div., Silver Spring, MD 20903-5640
G. C. Gaunaurd
Naval Surface Warfare Ctr., Carderock Div., White Oak, Silver Spring, MD 20903-5640
The acoustic scattering by a submerged spherical elastic shell near a free surface and insonified by plane waves at arbitrary angles of incidence is analyzed in an exact fashion by the classical separation of variables method. To satisfy the boundary conditions at the free sea surface, as well as on the surfaces of the elastic shell, the mathematical problem is formulated using the method of images. The scattered wave fields are expanded in terms of spherical wave functions using the addition theorems. The final results come out in terms of Wigner 3-j symbols or Clebsch--Gordan coefficients. Quite similar to the problem of scattering by multiple spheres, the computation of the scattered pressure field involves the solution of an ill-conditioned complex matrix system, of size that depends on the number of terms in the modal series required for convergence. This, in turn, depends on the value of the frequency and on the proximity of the steel shell to the free surface. The matrix equation is solved by the Gauss--Seidel method. Many backscattered echoes from the shell are computed, and its form function is displayed for various depths and in broad frequency intervals. The plots show that the large-amplitude, low-frequency resonance features in the sonar cross-sections shift upward as the shell approaches the free surface. This can be attributed to the decrease of added mass for the shell vibration. [Work partially supported by the Independent Research Program of the CDNSWC.]