Transition from sound‐soft to rigid behavior in scattering from submerged elastics shells over a broad frequency range

Abstract

We have determined previously that at suitably high frequencies elastic shells for a variety of thicknesses behave rigidly in the absence of narrow resonances. This observation was noted for thicknesses ranging from 1% to 2.5% for aluminum, steel, and WC for frequencies out to ka values of 300. Moreover, we have presented results at the low‐frequency end (low ka) that showed a distinct sound soft behavior for very thin shells in the absence of a resonance. This behavior persisted out to moderate values of ka. The procedure to determine whether a particular background was manifest to twofold. Firstly, the rigid or sound‐soft response is subtracted in appropriate partial wave space from the elastic response to determine the residual response. The residual response shows mainly resonance contributions at the resonance frequencies with little contribution otherwise. One can also examine the relative phase between the expected background and the elastic response and it should vary slowly except at a response where it varies rapidly with changing phase (a change of at least 180 deg). We here choose the case of a steel shell of thickness 0.3% of the radius of the shell and present results for the ka range from 0.0 to 500. Here the background is demonstrated to vary from sound‐soft at the lower end of ka to rigid at the upper end with no clear background in between.