Mechanisms of multi-bandgap inertial amplification applied in metamaterial sandwich plates

The design concept of integrating locally resonant metamaterials with sandwich plates has demonstrated promising prospects in the development of lightweight, load-bearing structures endowed with excellent capabilities for noise and vibration attenuation. However, achieving low-frequency vibration attenuation in the locally resonant metamaterial sandwich plates remains a challenging task that frequently requires the inclusion of additional centralized mass or heavy local resonators. This study proposes a novel multi-bandgap metamaterial sandwich plate with the lever-type inertial amplification mechanism (LIA-MMSP) for achieving the low-frequency vibration attenuation. Compared with the metamaterial sandwich plates incorporating multi-frequency local resonators (LR-MMSP) with equivalent additional mass, the LIA-MMSP exhibits the ability to achieve lower-frequency multiple bandgaps. The theoretical dynamic model is employed to elucidate the underlying mechanism behind the generation of multiple bandgaps at lower frequencies in the LIA-MMSP. The vibration attenuation performances of the LIA-MMSP are analyzed through both the finite element method and experiment study. The effect of various parameters on the vibration transmission characteristics of the LIA-MMSP is studied. The results show that the boundary frequencies of the LIA-MMSP are precisely one of the lever ratios of the LR-MMSP. By altering the lever ratio within the LIA-MMSP, precise fine-tuning and optimization of the low-frequency multiple bandgaps are achievable. When the attached mass is constrained, increasing the lever ratio enables the achievement of lower bandgaps. In addition, as the eigenfrequency of the primary lever-type IA resonator f_p and secondary lever-type IA resonator f_s decrease, both the first attenuation zone (AZ1) and the second attenuation zone (AZ2) of the LIA-MMSP shift towards lower frequencies. However, as f_p decreases, the width of AZ1 expands, and the minimum accelerations within the AZs decrease even further. Moreover, a normalized comparison provides validation of the exceptional performance of the proposed LIA-MMSP in terms of lightweight design, as well as its ability to achieve low-frequency broadband vibration attenuation.