Attenuation enhancement for the inertial amplification metamaterial using multiple local resonators

• Conditions for triple attenuation peaks in a single bandgap are derived. • The laws of coupled attenuation induced by multiple mechanisms are discussed. • High-attenuation supercell featuring multiple attenuation peaks is designed. The bandgap generated by inertial amplification metamaterial (IAM) features broad width and low-frequency, but weak attenuation strength within a large part of the bandgap. Introducing local resonators is the most common way to enhance low-frequency vibration attenuation characteristics. However, discrete bandgaps are usually observed for the metamaterials containing non-uniform resonators. In this paper, two resonators are attached to the baseline mass and the inertial amplifier of IAM, respectively. The merging of locally resonant bandgaps is realized by coupling them with the inertial amplification bandgap. The attenuation characteristics of the coupled bandgap are first studied, including the number and positions of attenuation peaks. Then, the methods to enhance the attenuation strength are explored. It is found that two attenuation peaks are attributed to zero effective stiffness while another one is induced by infinite effective mass. The conditions for the triple peaks occurring in a single bandgap are derived according to the rational polynomial form of the dispersion relation. Additionally, the attenuation strength within the coupled triple-peak bandgap is enhanced by increasing the mass of the resonator on the baseline mass and adjusting the coupling degree between the inertial amplification and the resonance of the local resonator on the inertial amplifier. Finally, to overcome the decrease in attenuation level when the attenuation-enhanced region widened, a supercell with high attenuation strength is designed by combining unit cells with different attenuation peaks. Compared to the IAM with double-peak bandgap in the previous study, the minimum attenuation level in the enhanced region is increased by 84%. This study gives guidance to enhance the attenuation characteristics of metamaterials in the low-frequency region.