  Elastic cylindrical shells are fitted with an internal mechanism which is
optimized so that, in the quasi-static regime, the combined system exhibits
prescribed effective acoustic properties. The mechanism consists of a central
mass supported by an axisymmetric distribution of elastic stiffeners. By
appropriate selection of the mass and stiffness of the internal mechanism, the
shell's effective acoustic properties (bulk modulus and density) can be tuned
as desired. Subsonic flexural waves excited in the shell by the attachment of
stiffeners are suppressed by including a sufficiently large number of such
stiffeners. Effectiveness of the proposed metamaterial is demonstrated by
matching the properties of a thin aluminum shell with a polymer insert to those
of water. The scattering cross section in water is nearly zero over a broad
range of frequencies at the lower end of the spectrum. By arranging the tuned
shells in an array the resulting acoustic metamaterial is capable of steering
waves. As an example, a cylindrical-to-plane wave lens is designed by varying
the bulk modulus in the array according to the conformal mapping of a unit
circle to a square.
