Biharmonic Split Ring Resonator Metamaterial: Artificially dispersive effective density in thin periodically perforated plates

@article{Farhat2014BiharmonicSR,
  title={Biharmonic Split Ring Resonator Metamaterial: Artificially dispersive effective density in thin periodically perforated plates},
  author={Mohamed Farhat and Stefan Enoch and S{\'e}bastien Guenneau},
  journal={arXiv: Materials Science},
  year={2014}
}
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… 

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