Controlling the propagation of flexural elastic waves with ceramic metatiles

In this work, we examine the application of phononic metamaterials for elastic impact noise insulation in tiled flooring, through the development of an innovative ceramic metatile that incorporates phononic crystals with optimized joint configurations. First, we optimize the geometrical and material parameters of the proposed metatile, which is composed of small ceramic subtiles connected by silicon joints, in order to reduce longitudinal and flexural wave propagation on tiled floors, which are responsible for noise vibrations in tiled environments. A bandgap is achieved that effectively suppresses the transmission of impact noise through the periodic structural configuration. For flexural waves, the ceramic metatile exhibits a pronounced attenuation of wave transmission in the range of $500$-$1900$ Hz along the $[100]$ direction, and $500$-$1400$ Hz along the $[110]$ direction. For longitudinal waves, a broad bandgap is observed, spanning from $400$ Hz to $1950$ Hz in both the $[100]$ and $[110]$ directions. Additionally, the bandgaps shift toward lower frequencies with increasing width of the subtiles and silicon joints, or with a decrease in the Young's modulus of the silicon. In both experimental and numerical tests, it is demonstrated that the integration of silicon joints inside the ceramic metatile improves the acoustic insulation performance, as measured by the reduction of impact noise levels across a wide range of low frequencies. The findings highlight the potential of metamaterials in architectural acoustics, offering innovative solutions for elastic wave control in tiled environments.