### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 2aSA3. The exact sonar cross section of an elastic spherical shell near
the sea surface.

**H. Huang
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*Naval Surface Warfare Center, Indian Head Div., Silver Spring, MD
20903-5640
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**G. C. Gaunaurd
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*Naval Surface Warfare Ctr., Carderock Div., White Oak, Silver Spring, MD
20903-5640
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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.]