  We present in this paper a theoretical and numerical analysis of bending
waves localized on the boundary of a platonic crystal whose building blocks are
split ring resonators (SRR). We first derive the homogenized parameters of the
structured plate using a three-scale asymptotic expansion in the linearized
biharmonic equation. In the limit when the wavelength of the bending wave is
much larger than the typical heterogeneity size of the platonic crystal, we
show that it behaves as an artificial plate with an anisotropic effective Young
modulus and a dispersive effective mass density. We then analyze dispersion
diagrams associated with bending waves propagating within an infinite array of
SRR, for which eigen-solutions are sought in the form of Floquet-Bloch waves.
We finally demonstrate that this structure displays the hallmarks of
All-Angle-Negative-Refraction(AANR) and it leads to superlensing and
ultrarefraction effects, interpreted thanks to our homogenization model as a
consequence of negative and vanishing effective density, respectively.
