The low-frequency and broadband pendulum metamaterials based on inertial amplification mechanism

Pendulum has recently been introduced into the field of elastic metamaterials because of its low-frequency vibration characteristic, which further expands the application value of such structure. However, the low-frequency and broadband performance of traditional pendulum (TB) metamaterials still need to be further improved. In this paper, a new low-frequency pendulum metamaterial is proposed, and the low-frequency elastic wave propagation characteristics of the metamaterial are studied. The study shows that compared with the TB metamaterial, it can effectively lower the bandgap (BG) of metamaterial, but greatly narrow the BG. To solve this problem, the negative inertial amplification mechanism is further proposed, and the variation law of the metamaterial BG under this mechanism is investigated. It is found that the mechanism can effectively broaden the metamaterial BG and in specific cases make it have infinite width. Meanwhile, the constraint relationship between the frequency response function of unit-cell structure and the wave vector of metamaterial is established, which is used to reveal the broadening rationale of the BGunder the negative inertial amplification mechanism. Finally, depending on the negative inertial amplification mechanism, a novel broadband pendulum metamaterial is designed based on the low-frequency pendulum metamaterial. The relationship between the broadband attenuation behavior of the metamaterial and the frequency response function of unit-cell structure is analyzed, the working mechanism of negative inertial amplification to broadband pendulum metamaterial is also discussed, and the relevant optimization design method is given at the end.