Dispersion analysis of periodic hourglass-shaped metamaterials for wave propagation

Abstract

This study reports numerical modeling of phononic-based crystals with the hourglass lattice periodically arranged in 2D space. The investigated resonant elements include dome shape metastructure as well as their various combinations, in particular, hourglass configurations. The mechanical wave band structure and transmission characteristics of such systems have been computed using finite element simulations performed in Comsol multiphysics. The general concept of a locally resonant phononic crystal is proposed. The concept utilizes elastic wave resonances to form constructive or destructive interference, which creates ranges of frequencies at which waves are either allowed to propagate (pass bands) or block in one (stop bands) or any direction (complete band gaps). The bandgap depends on the configuration of the periodic structure, the material of scattering unit, and that of a host matrix, which has been explored in this study. The unit cell consists of hourglass-shaped resonators repeated in two orthonormal directions, making it a 2D phononic meta material. The existence of a separate attenuation mechanism associated with the hourglass resonant elements that increase performance in the lower frequency regime has been identified. The results show formation of broadband gaps positioned significantly below the first Bragg frequency. The most optimal configuration is the crystal for low-frequency broadband attenuation, where each scattering unit is composed of multiple hourglass-based resonators. This system forms numerous gaps in the lower frequency regime, below Bragg bands, while maintaining a reduced crystal size viable for vibration isolation technology. The finding opens alternative perspectives for the construction of vibration mitigation in the low-frequency range, usually inaccessible by traditional means, including conventional phononic crystals.