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In order to achieve the attenuation of low‐frequency sound, in this paper, a hybrid metamaterial structure with a complete band gap below 500 Hz is proposed, which is subjected to second‐order fractal, series fusion, and whether the structure is framed or not to form 8 different structures. Based on the finite element method and Bloch's theorem, the bandgap and transport properties of all model structures are evaluated, and the bandgap and propagation properties of metamaterial structures with different fractal levels are elucidated in terms of band structure and group velocity. In addition, the third‐order fractal structure and the dependence of the band gap on the material are also studied. The results show that the structure has a superior band gap width, and the complete band gap of its tandem fusion structure accounts for up to 45.502% in the range of 500 Hz, and the second‐order fractal has a complete band gap of 45.588% in the range of 1000 Hz. Compared with other structures, it can produce lower and better band gap. The research in this paper provides a new strategy for realizing acoustic metamaterial structures with low frequency band gaps. [ABSTRACT FROM AUTHOR]

From periodically cutting off rods in two-dimensional lattice grids, we find an easy and feasible way to control elastic bandgaps (BGs) in them. Due to the periodical cut-off (PCO) operations, the exposed cantilevers lose the static load-supporting ability; however, their mass distribution and inertia significantly affect the propagation of elastic waves. We first give several PCO types for square and triangular lattice grids. Then a detailed finite-element method for the calculation of elastic BGs is described. The BGs in the hexagonal-type PCO triangular lattice grid are studied for example. Localized resonant BGs are found and predicted. Frequency responses of the finite specimen are also analyzed to support our conclusions. Sketches of three kinds of PCO lattice grids: the PCO square lattice grid (left), the hex-type PCO triangular lattice grid (center), and the Kagomé-type PCO triangular lattice grid (right). [ABSTRACT FROM AUTHOR]