Reflection and Transmission of Sound by Elastic Spherical Shells

The sound fields resulting from a plane wave incident on a spherical elastic shell are found. Both the internal and external fields due to the shell are considered and compared with well-known results. The Rayleigh limit is discussed, and it is found that the external field is similar to that produced by a rigid sphere but with more complicated coefficients. The internal field is of a complicated nature but reasonable to consider for numerical computation. The sound fields for a hemispherical shell mounted on a rigid medium are obtained by the image method. Numerical results for the sound intensity at the center of the hemisphere are presented for various elastic materials.