Theory of the background amplitudes in acoustic resonance scattering

For problems of resonance scattering of acoustic waves from penetrable targets of canonical geometry, a general approach which yields an exact and simple expression, named the inherent background coefficient, for the acoustical background is proposed. By analyzing the effect of the structural damping of targets, it is found that, within each modal surface admittance of targets, including a negligible effect of the structural damping, there are two interacting contributions: a constant contribution and a resonant contribution. The constant contribution, which corresponds to the inherent background coefficient, can be obtained from the zero-frequency limit of an equivalent fluid target. For targets including a significant effect of the structural damping, the inherent background depends on the damping effect. The inherent background coefficients for empty, elastic, spherical shells not including the structural damping effect are shown explicitly. The coefficients are described by a generalization of the fluid-loading parameter. Also, it is analytically and numerically shown that the inherent background undergoes a transition to the rigid or soft background in the appropriate limit, and correctly describes the acoustical background for any shell over all frequencies.