Band gaps and vibration transfer characteristics of one-dimensional triangular arrangement of elastic metamaterials

In this paper, three one-dimensional elastic metamaterials (EMs) coupled with triangular arranged resonators are proposed for broadband elastic vibration suppression and the vibration characteristics of these three models (MODELS II, III, and IV) are compared with the classical EM MODEL I. Firstly, the dispersion curves of the proposed models are studied based on Bloch's theorem. This shows that the starting frequency of the first band gap for MODEL II, MODEL III, and MODEL IV is 8.8%, 54%, and 15% lower than that of MODEL I, respectively. The total band gap width of MODEL IV (α = 60°) is 2.89 times that of MODEL II (α = 60°), 1.59 times that of MODEL III (α = 60°), and 4.3 times that of MODEL I, specifically. The effect of the parameters and configuration of the system on the band gap features is discussed. The spring stiffness ratio has the greatest influence on the band gap behavior, and the optimal parameters of a low-frequency vibration isolation design are obtained accordingly. Finally, the wave propagation characteristics of the EM system composed of finite unit cells show great agreement with the band gap structure of an infinite lattice structure predicted by Bloch's theorem. This research will provide important clues and theoretical guidance for the design of vibration isolators, plates, beams, and other renewed devices. (paper)