Zero‐Frequency Bandgap Metamaterials: The Mosaic Design Strategy

Abstract Bandgaps constitute the central feature of photonic and phononic crystals. However, the zero‐frequency bandgap, defined here as the absence of wave states from 0+ to a finite frequency, is generally regarded as not realizable for the Bragg mechanism since the lattice constants need to be very large to infinite. Moreover, a structure or material that displays a zero‐frequency bandgap would present a challenge to the theory of homogenization, which is predicated on the existence of low‐frequency, long‐wavelength excitations, for which the effective material parameters apply. In this work, the finite‐sized tiles are utilized, linked together at their corners, to create a mosaic plate system that can display static rigidity with translational degrees of freedom. Full waveform simulation results on the mosaic plate show a clear zero‐frequency bandgap, which are verified experimentally by laser vibrometer scanning of modes excited by a harmonic point source, as well as by comparison of sound transmission loss (TL) between the mosaic plate and a uniform plate with similar mass density. The latter comparison shows the mosaic plate to have a 13 dB advantage in TL at 50 Hz, and deviates from the mass density law over a broad low‐frequency range.