Classification of resonances in the scattering from submerged spheroidal shells insonified at arbitrary angles of incidence

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Abstract
A numerical study is presented for plane-wave scattering from thin steel spheroidal shells in the frequency region corresponding to the onset of resonances. Arbitrary incidence angles are allowed for, in order to analyze the possible aspect-angle dependence of resonances. Both monostatic angular distributions and backscattered echoes are examined as a function of the nondimensionalized quantity kL/2, where the wavenumber k is 2π/λ and L is the length of the spheroid. Shell thickness is chosen to be very thin so that the physical mechanisms involved in the process can be isolated. In the analysis and in the absence of a resonance, only ‘‘background’’ effects associated with soft-body scattering are observed (due to the very small thickness of the shell), while a characteristic coherent effect is observed in the resonance region. Analysis of the exact theoretical predictions leads to the conclusion that elastic resonances for these objects correspond to modal, vibrational, surface standing waves at discrete frequencies with a relatively fixed phase velocity. Moreover, the surface standing-wave interpretation leads to simple semiphenomenological expressions that can reliably predict the resonance locations. Furthermore, the study leads to the conclusion that only two modes of vibration are allowed, namely those along the axis of symmetry and those perpendicular to it. Thus only two classes (or modes) of resonances exist, corresponding to surface standing waves along and perpendicular to the spheroid’s axis of symmetry. This property can be exploited to elicit geometrical (and to some extent material) characteristics of the object from its echo, in particular, its length-to-diameter or aspect ratio L/D.

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