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

Abstract

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.

Low frequency broadband bandgaps in elastic metamaterials with two-stage inertial amplification and elastic foundations

“…Recently, improved mass-spring lattice models based on the inertial amplification structure have been proposed. Li et al constructed EMs coupled with triangular arranged resonators [51] and EMs with a type of scissor-like structure [52], which respectively achieving a certain degree of improvements in bandgap characteristics. Banerjee et al constructed an inertial amplified chain by attaching the levered mass and the resonant mass separately to the base, which exhibits double-attenuation bandgaps [53].…”

Gradient continuum model of nonlocal metamaterials with long-range interactions

“…As significant advances in engineering structures, metamaterials have attracted increasing attention for their applications in controlling wave propagation and vibration reduction [1][2][3]. Metamaterials are composed of artificial periodic structures that are designed to achieve novel physical properties, such as an effective negative mass [4][5][6], negative refraction [7,8] and topological effects [9,10].…”

Bandgap merging and widening of elastic metamaterial with heterogeneous resonator

“…Therefore, much effort has been devoted to exploring broad bandgap in low frequency with limited mass by various EMs structural designs. We discussed the influences of different coupling modes between main mass and resonator in triangular arrangement EMs to obtain ultrabroad and ultra-low bandgap [18]. It is attempted that the attenuation bandwidth can be extended by multiple resonators to cover a range of frequencies, which is called the multi-cell synergetic coupling resonance mechanism [19].…”