Low-frequency bandgaps for water waves enabled by flexible plate metamaterials

This study investigates a novel class of flexible plate metamaterials (FPMMs), consisting of a periodic array of bottom-mounted flexible structures, designed for the sub-wavelength manipulation of surface gravity waves. A theoretical framework is developed by coupling the matched eigenfunction expansion method with a modal expansion technique, incorporating Bloch’s theorem to characterise the band structures and complex dispersion relations. Numerical analysis reveals that the structural flexibility facilitates the formation of low-frequency, broadband bandgaps, primarily driven by a local resonance (LR) mechanism. It is shown that wave propagation can be effectively suppressed within these bandgap regimes through the synergistic interaction between the incident wave field and the structural vibration modes. The theoretical predictions are validated through laboratory experiments conducted in a wave flume, where substantial wave attenuation was observed under resonant conditions. Notably, the LR-induced bandgaps occur at significantly lower frequencies and exhibit broader bandwidths compared to those arising from traditional Bragg resonance. These findings demonstrate that the proposed FPMMs provide a tunable and effective mechanism for sub-wavelength wave attenuation, offering fundamental insights into localised hydrodynamic wave control.