Numerical models for problems of acoustic scattering by thin elastic shells immersed in fluids

This paper presents relatively simple formulations of the problem of acoustic scattering by flooded and hollow elastic shells immersed in fluids, which can serve as a basis for efficient numerical models. The full rigorous formulation of the problem, which involves the Helmholtz equations for acoustic pressures in the fluids and the Navier equation for three-dimensional displacements in the elastic material, is reduced to a boundary value problem only for the Helmholtz equations with effective boundary conditions relating the boundary pressures and normal displacements on both sides of the shell. To that end, the thin elastic shell is regarded as a neighborhood of its midsurface, and the boundary values of the elastic quantities (displacements and stresses) are expressed via their expansions about the midsurface, considering the shell thickness as a small parameter. In this paper, the expansion is restricted to the first order. Despite relative simplicity, the first-order models can describe elastic effects rather well, which is demonstrated by the comparison with the exact solutions for the case of spherical elastic shells. In particular, the boundary element method numerical solutions reproduce the low-frequency resonant peaks and dips of the exact solutions.