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 and secondary lever-type IA resonator decrease, both the first attenuation zone (AZ1) and the second attenuation zone (AZ2) of the LIA-MMSP shift towards lower frequencies. However, as 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.

中文翻译：

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多带隙惯性放大应用于超材料夹层板的机理


将局部谐振超材料与夹层板集成的设计理念在开发具有优异的噪声和振动衰减能力的轻质承载结构方面展现出了广阔的前景。然而，在局部谐振超材料夹层板中实现低频振动衰减仍然是一项具有挑战性的任务，通常需要包含额外的集中质量或重型局部谐振器。本研究提出了一种具有杠杆式惯性放大机构（LIA-MMSP）的新型多带隙超材料夹层板，用于实现低频振动衰减。与具有同等附加质量的包含多频局部谐振器（LR-MMSP）的超材料夹层板相比，LIA-MMSP表现出实现低频多带隙的能力。采用理论动态模型来阐明 LIA-MMSP 中低频下多个带隙生成背后的基本机制。通过有限元方法和实验研究对LIA-MMSP的减振性能进行了分析。研究了各种参数对LIA-MMSP振动传递特性的影响。结果表明，LIA-MMSP 的边界频率恰好是 LR-MMSP 的杠杆比之一。通过改变 LIA-MMSP 内的杠杆比，可以实现低频多带隙的精确微调和优化。当附着质量受到约束时，增加杠杆比可以实现更低的带隙。 此外，随着初级杠杆型IA谐振器和次级杠杆型IA谐振器的特征频率降低，LIA-MMSP的第一衰减区(AZ1)和第二衰减区(AZ2)均向较低频率移动。然而，随着减小，AZ1 的宽度扩大，并且 AZ 内的最小加速度进一步减小。此外，归一化比较验证了所提出的 LIA-MMSP 在轻量化设计方面的卓越性能，以及其实现低频宽带振动衰减的能力。