SCATTERING OF A PLANE ACOUSTIC-WAVE BY A SPHERICAL ELASTIC SHELL NEARA FREE-SURFACE

The acoustic scattering by a submerged spherical elastic shell near a free surface, which is insonified by plane waves at arbitrary angles o f incidence is analyzed in an exact fashion using the classical separa tion of variables technique. To satisfy the boundary conditions at the free surface as well as on the surface of the spherical elastic shell , the mathematical problem is formulated using the image method. The s cattered wave fields are expanded in terms of the classical modal seri es of spherical wave functions utilizing the translational addition th eorem. Quite similar to the problem of scattering by multiple spheres, numerical computation of the scattered wave pressure involves the sol ution of an ill-conditioned complex matrix system the size of which de pends on how many terms of the modal series are required for convergen ce. This in turn depends on the value of the frequency, and on the pro ximity of the spherical elastic shell to the free surface. The ill-con ditioned matrix equation is solved using the Gauss-Seidel iteration me thod and Twersky's method of successive iteration cross checking each other. Backscattered echoes from the spherical elastic shell are exten sively calculated and displayed. The result also demonstrates that the large amplitude low frequency resonances of the echoes of the submerg ed elastic shell shift upward with proximity to the free surface. This can be attributed to the decrease of added mass for the shell vibrati on. The present benchmark solution could eventually be used to validat e those found by numerical schemes.