Negative index metamaterial through multi-wave interactions: numerical proof of the concept of low-frequency Lamb-wave multiplexing.

We study numerically the potential of a multimodal elastic metamaterial to filter and guide Lamb waves in a plate. Using a sub-wavelength array of elongated beams attached to the plate, and combining the coupling effects of the longitudinal and flexural motion of these resonators, we create narrow transmission bands at the flexural resonances of the beams inside the wide frequency bandgap induced by their longitudinal resonance. The diameter of the beams becomes the tuning parameter for selection of the flexural leakage frequency, without affecting the main bandgap. Finally, by combination of the monopolar and dipolar scattering effects associated with the coupled beam and plate system, we create a frequency-based multiplexer waveguide in a locally resonant metamaterial.