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Cloaks for underwater applications designed for actual submarine acousticstealth are still far from the technological advancement needed for being putin practice. Several challenges are to be overcame such as dealing with weightor non-axisymmetric shapes. In this paper, we introduce the use of ellipticalcoordinates to define quasi-symmetric transformations to retrieve the materialproperties of pentamode cloaks for elliptical shaped targets, along with aquantifiable approximation introduced by the rotation tensor being differentfrom the identity. This is done analitically adopting transformation theory, inan attempt to generalize the usual approach for axisymmetric cloaks, with theaim of dealing with shapes closer to those of the actual cross section of asubmarine. With respect to existing techniques for dealing with arbitrarilyshaped pentamode cloaks, the introduced technique allows for a priori controlon the principal directions of anisotropy and for enlarged design space interms of possible combinations of material property distributions for the samegeometry of the problem.

Acoustic scattering reduction of elliptical targets via pentamode near-cloaking based on transformation acoustics in elliptic coordinates