Abstract
A null field T‐matrix formalism is developed and used to calculate scattering of a pressure wave from a fluid‐loaded elastic spherical shell in proximity to a rough fluid–elastic interface. The Helmholtz–Kirchhoff integral representations of the various scattered pressure and displacement fields are constructed. The surface fields are required to satisfy the elastic boundary conditions and the scattered fields are required to satisfy the extended boundary condition. The free‐field T matrices for the elastic shell and the rough fluid–elastic interface are constructed and used in the Helmholtz–Kirchhoff and the null field equations for the shell‐interface system. It is shown that the T matrix for the system is simply related to the free‐field T matrices for the shell and the rough fluid–elastic interface. A perturbative solution is obtained for scattering from arbitrary roughness, and an ‘‘exact’’ solution is obtained for scattering from periodic roughness. The ‘‘exact’’ solution is used to obtain a variety of numerical results that show some of the effects of the acoustic coupling that occurs between the rough interface and the elastic spherical shell.
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