Abstract:
A null field T-matrix formalism is developed and used to calculate plane-wave scattering from a fluid loaded elastic spherical shell in proximity to sound hard, sound soft, fluid--fluid, and fluid--elastic interfaces with periodic surface roughness. For each type of interface, the Helmholtz--Kirchhoff integral representation of the various scattered pressure and displacement fields are constructed; the surface fields are required to satisfy the appropriate boundary conditions and the scattered fields are required to satisfy the extended boundary condition. Spherical basis functions are used to construct a free field T-matrix for the elastic shell and rectangular vector basis functions are used to construct a representation of the free field T-matrix for the rough interface. The free field T-matrices are introduced into the Helmholtz--Kirchhoff equations for the scattered fields and the null field equations for the shell-interface system and an ``exact'' analytical solution is obtained. Numerical results are obtained that demonstrate the effects of boundary type, elastic parameters, roughness geometry, amplitude, and slope on the scattered pressure field and on the ability to ``see'' the scatter from the elastic shell.