Fluid-structure effects of cloaking a submerged spherical shell

Abstract

Backscattering from a cloaked submerged spherical shell is analyzed in the low, mid, and high frequency regimes. Complex poles of the scattered pressure amplitudes using Cauchy residue theory are evaluated in an effort to explain dominant features of the scattered pressure and how they are affected by the introduction of a cloak. The methodology used is similar to that performed by Sammelmann and Hackman [J. Acoust. Soc. Am. 85, 114–124 (1989); J. Acoust. Soc. Am. 89, 2096–2103 (1991); J. Acoust. Soc. Am. 90, 2705–2717 (1991)] in a series of papers written on scattering from an uncloaked spherical shell. In general, it is found that cloaking has the effect of diminishing the amplitude and shifting tonal backscatter responses. Extreme changes of normal and tangential fluid phase velocities at the fluid–solid interface when cloaking is employed leads to elimination of the “mid-frequency enhancement” near the coincidence frequency for even modestly effective cloaks, while reduction of the “high-frequency enhancement” resulting from the “thickness quasi-resonance” near the cut-off frequency of the symmetric (SB2 ) mode requires more effective cloaking, but can be practically eliminated by employing a cloak that creates tangential acoustic velocities in excess of the SB2 mode phase speed near cutoff.