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Radial sonic crystals (RSC) are fluidlike structures infinitely periodicalong the radial direction. They have been recently introduced and are onlypossible thanks to the anisotropy of specially designed acoustic metamaterials[see Phys. Rev. Lett. {\bf 103} 064301 (2009)]. We present here a comprehensiveanalysis of two-dimensional RSC shells, which consist of a cavity defectcentered at the origin of the crystal and a finite thickness crystal shellsurrounded by a fluidlike background. We develop analytic expressionsdemonstrating that, like for other type of crystals (photonic or phononic) withdefects, these shells contain Fabry-Perot like resonances and stronglylocalized modes. The results are completely general and can be extended tothree dimensional acoustic structures and to their photonic counterparts, theradial photonic crystals.

Acoustic resonances in two dimensional radial sonic crystals shells