Broadening band gaps of shear horizontal waves of metamaterials via graded hierarchical architectures

Abstract A new kind of graded hierarchical phononic crystal is proposed to broaden the band gaps of shear horizontal (SH) waves. The architectures are constructed with graded unit cells composed of various levels of hierarchical structures. The hierarchical coupling band gaps can be separated with the help of a multi-scale homogenization technique, and the corresponding relationship between band gaps on each hierarchy and equivalent structure with single periodicity is established. The effect of main structural parameters on the band structure of the proposed architecture is investigated by numerical simulations. Results show that the graded hierarchical phononic crystal can generate extremely broad band gaps with appropriate parameters. Two mechanisms of broadening band gaps are also revealed. On one hand, the local periodicity within the higher hierarchies enlarges band gaps by overlapping the cross-hierarchical gaps in the high frequencies. On the other hand, the graded configuration within the supercell breaks some translational symmetries and creates more band gaps in the low frequencies by opening the Dirac cone of the band structure, and the newly created band gaps are merged to the original band gaps to form a wider band gap.