Acoustic scattering from fluid-filled, concentric, submerged, cylindrical, elastic shells

Abstract

The present study addresses the scattering of plane (cw) sound waveforms by concentric, fluid-filled, elastic shells in water from the viewpoint of an impedance-based formulation. For a single fluid-filled shell, this impedance formulation is shown to agree with (the exact form of) the earlier resonance scattering theory (RST) which used elastic potentials and matches various stresses and displacements at the boundaries. The comparison cannot be established for more than one (concentric) shell, since there is no RST formulation for such cases. However, the present formulation is used to generate predictions for double shells with various fillers. A number of conclusions emerge from the present analysis and calculations, particularly for the case of two concentric fluid-filled shells. In this instance, if the filler of the annular region in between the shells is air, then the structural components inside that region do not contribute to the scattered field, and can be safely ignored. For a water-filled annular region, the total backscattering form function (at θ=π) will automatically display the isolated shell resonances, without any need for any ‘‘background’’ subtraction. Furthermore, the total angular form functions, evaluated at resonance, will exhibit the typical shape of rhodonea patterns, again without subtracting any type of background. These cases in which background subtraction is not needed are contrasted with various others in which it is needed, and how resonance isolation is achieved in all cases considered is shown. Many computer generated graphs for single and double shells illustrate all these points.