Interpretation of the three-dimensional sound fields scattered by submerged elastic shells and rigid spheroidal bodies

Abstract

The direct scattering problem associated with submerged spheroidal targets at frequencies within their resonance regime is studied. The incident waves are plane and continuous, and the composition of the spheroid can be either impenetrable or penetrable. In the impenetrable case, the body is assumed rigid. In the penetrable case, the target is an elastic shell, whose motion is governed by the exact three-dimensional equations of linear elastodynamics. The aspect ratio of the spheroids takes on values from L/D=1.5–30. The method used in the calculations is the extended boundary condition (EBC) or T-matrix method. The target’s form function or scattering angular pattern in the farfield versus monostatic variable angles of incidence at fixed frequencies (i.e., monostatic angular plots), or versus frequency, at fixed directions of observation (i.e., backscattering responses), is displayed. The graphs exhibit the versatility of the EBC method, particularly in cases, such as for the elastic shell, in which analytic solutions are not possible. The case of an elastic shell is considerably more difficult than that of any impenetrable or solid elastic spheroid. The aspect ratio analyzed here for a shell is at the current upper limit of performance of the computational method used in our analysis. Various resonance effects in the displayed plots are studied, particularly the resonance isolation process present in the backscattering responses and the connection to combinations of Legendre functions observable in the angular plots. The relative values of the creeping-wave levels and those due to specular reflections are also compared. For very elongated spheroids, the creeping wave levels seem to be stronger(!). Calculated predictions are displayed, and an explanation of this interesting situation is offered.