Study on the vibration suppression mechanisms of the lightweight flexible metamaterial sticker with non-independent resonators

The working mechanism of an acoustic metamaterial (AM) for broadband elastic vibration suppression with non-independent local resonators is presented in this paper along with the general formulas for the effective mass (EM), dispersion relation, and transmission spectrum (TR) of this metamaterial unit. A kind of flexible metamaterial sticker that is lightweight and skillfully uses flexible materials is proposed based on a theoretical approach. The flexible metamaterial sticker has a surface density of only 2.22 kg/m2 and an overall thickness of only 3 mm. It is made by depositing the flexible cylindrical supports in a square lattice pattern on the surface of the flexible plate. The finite element method (FEM) was used to systematically investigate the band structures, frequency response function (FRF), dynamic effective mass density (EMD), as well as the formation mechanisms of the flexural vibration bandgaps (FVBGs) of the metamaterial plates (composite structure after applying the metamaterial sticker). Additionally, a thorough analysis was conducted on the impacts of geometrical parameters (the rubber cylinder thickness, the flexible material plate thickness, the lattice constant, and the rubber cylinder radius) on the FVBGs. Finally, an overall vibration attenuation for the proposed metamaterials was estimated by using the spatial quadratic velocity and experiment. The findings confirmed that the AM caused multi-frequency negative EM, while the overall bandgap width was substantially wider than that of conventional metamaterials. Due to the numerous vibration modes of the flexible metamaterial, the suggested flexible lightweight metamaterial sticker can generate several observable local resonance FVBGs in the low-frequency range. Significantly broadening the bandwidth of FVBGs can be achieved by varying the rubber cylinder radius and thickness, as well as by adjusting the lattice constant and flexible material plate thickness. Within the FVBGs, the proposed lightweight flexible metamaterial sticker shows a good vibration-suppression performance, when compared with the traditional damping structure or metamaterials.