Metamaterial sandwich plates with two-degree of freedom inertial amplified resonators for broadband low-frequency vibration attenuation
Lei Gao, Cheuk Ming Mak, Chenzhi Cai, Supeng Deng
Abstract
Sandwich plates are extensively utilized across various fields, encompassing building engineering, mechanical engineering, and aerospace engineering, owing to their exceptional stiffness-to-weight ratio. However, effectively attenuating the low-frequency and broadband vibrations of these plates poses a significant challenge. This paper proposes a new type of metamaterial sandwich plate that incorporates two-degree of freedom inertial amplified resonators (IA-MSPDF2), to attain two low-frequency band gaps (BGs) and achieve broadband vibration attenuation. The dispersion relation of the IA-MSPDF2 is calculated based on the Bloch-Floquet theorem, and the generation mechanism of two low-frequency BGs is analyzed through eigenmodes. Both numerical and experimental studies are conducted to substantiate the advantages associated with the presence of two BGs in the IA-MSPDF2 design. The results show that the enhanced coupling effect between the primary and secondary resonators of the IA-MSPDF2 leads to the band associated with the local resonance that shifts to lower frequencies, resulting in a Bragg scattering BG that arises above the locally resonant BG. Compared to the metamaterial sandwich plate with one-degree of freedom inertial amplified resonators (IA-MSPDF1) of equal mass, the IA-MSPDF2 exhibits an increased relative bandwidth of BG by 15%. Increasing the damping of the inertial amplified resonator causes two attenuation zones to widen and merge into a wider attenuation zone. The proposed IA-MSPDF2 can robustly and effectively attenuate the low-frequency and broadband vibration with a small mass cost, contributing to the further exploration and utilization of metamaterial sandwich plates in engineering applications.