Acoustic Scattering by an Axisymmetric Thin Elastic Shell

Abstract

A technique is presented for predicting acoustic scattering by an axisymmetric, but otherwise generally shaped, thin elastic shell immersed in an infinite ideal homogeneous fluid. It is assumed that the shell is illuminated by a monochromatic plane wave and that linearity and the thin-shell theory are applicable. The problem is formulated by coupling the Lagrangian equations of motion for the shell to the surface Helmholtz integral equation. In this problem, both the surface pressure and the body displacements are unknowns. The pressure and displacements are expressed in terms of subsectional basis functions where the coefficients of the displacement basis functions become the generalized coordinates of the system. In this manner the integro-differential equations are reduced to a set of linear algebraic equations, which are then solved. Finally, farfield pressure is computed from which the bistatic scattering pattern is found. Numerical results are obtained for sperhical and hemispherically capped cylindrical shells. The numerical results for the spherical shell are compared with the exact analytic solution for that geometry. This comparison serves as a test of the validity of the technique. [Supported by Cornell Aeronautical Laboratory, Internal Research.]