Scattering and active acoustic control from a submerged spherical shell

This paper is concerned with the scattering from a submerged (heavy fluid) bilaminate spherical shell composed of an outer layer of steel, and an inner layer of radially polarized piezoelectric material. The methodology used includes separation formulas for the stresses and displacements, which in turn are used (coupled with spherical harmonics) to reduce the governing equations to linear systems of ordinary differential equations. This technique uses the full equations of elasticity rather than any of the various thin-shell approximations in determining the axisymmetric scattering from a shell, normal modes of vibration for the shell, as well as voltages necessary for annihilation of a scattered pressure due to insonification of the shell by an incident plane wave.