Acoustic resonance scattering by a system of concentrically multilayered shells: the inherent background and resonance coefficients

The inherent background coefficients that exactly describe the background a mplitudes in the scattered field have been presented for the scattering of plane acoustic waves by a system of concentrically multilayered solid and/o r fluid shells submerged in a fluid. The coefficients have been obtained by replacing the mechanical surface admittance function with the zero-frequen cy limit of the admittance function for the analogous fluid system, where t he shear wave speeds in the solid layers are set to zero. By taking advanta ge of the concept of incoming and outgoing waves, we find the surface admit tance function for the fluid system in such a form that the analytical gene ralization for any number of layers and the physical interpretation are ver y easy. The background coefficients obtained are independent of the bulk wa ve speeds in the system: they depend on the mass densities and the thicknes ses of the shells. With increasing frequency, the inherent background under goes a transition from the soft to the rigid background. The transition fre quency fbr the spherical system is lower than that for the cylindrical syst em, but the difference becomes negligible in high order partial waves. The resonance coefficients that directly describe the resonance amplitudes in t he scattered field are also found, and the validity of the analysis is nume rically demonstrated for the case of empty spherical shells of rubber-coate d steel and aluminum submerged in water.