Theory of elastic resonance excitation by sound scattering

TLDR

The resonance formalism of nuclear‑reaction theory is applied to sound scattering from submerged elastic bodies such as cylinders and spheres. The scattering cross section fluctuates because a superposition of narrow resonances in the normal modes, which shift with frequency, interferes with a rigid‑body background, producing π‑phase jumps at each resonance. The body is largely impenetrable except near its eigenfrequencies, where resonances with widths inversely determining decay times generate angular nulls linked to the rigid‑body cross section.

Abstract

The resonance formalism of nuclear-reaction theory is applied to the problem of sound scattering from submerged elastic bodies (illustrated here by circular cylinders and spheres). It is demonstrated that the strongly fluctuating behavior of, e.g., the backscattering cross section is caused by a superposition of generally narrow resonances in the individual normal modes (partial waves), which move up in frequency from one partial wave to the next, corresponding to a series of creeping waves (’’Regge poles’’), and which are superimposed on a background of rigid-body (potential) scattering. This fact, together with a resonance representation of the elastic field in the interior, indicates that the elastic body is relatively impenetrable to the incident wave except in the vicinity of the resonances, which occur at the eigenfrequencies of the elastic vibrations of the body. Various types of interference between resonance and background are analyzed, and the phase of the partial wave is shown to undergo a jump of π at each resonance. Decay times (ringing) of the excited resonances are found to depend inversely on their width, and the appearance of nulls in the scattering angular distribution at certain resonances is related to the cross section of the rigid body.