Metamaterial sandwich plates with two-degree of freedom inertial amplified resonators for broadband low-frequency vibration attenuation

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-MSP_DF2), to attain two low-frequency band gaps (BGs) and achieve broadband vibration attenuation. The dispersion relation of the IA-MSP_DF2 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-MSP_DF2 design. The results show that the enhanced coupling effect between the primary and secondary resonators of the IA-MSP_DF2 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-MSP_DF1) of equal mass, the IA-MSP_DF2 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-MSP_DF2 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.