Tailoring vibration suppression bands with hierarchical metamaterials containing local resonators

Abstract

Vibration suppression at subwavelength scales is of great interest in acoustic and/or elastic metamaterial engineering which has a wide range of potential applications requiring dynamic stabilities by using light-weight structures and materials. In this study, we propose the concept of metamaterials with hierarchically organized local resonators, which possess the ability to efficiently tailor elastic wave or vibration attenuation to various frequency regions through different hierarchical designs. Wave dispersion relations and band gap behaviors of one-dimensional lumped mass-spring hierarchical metamaterials are characterized first with outward and inward hierarchical configurations. A honeycomb hierarchical lattice with embedded rubber-coated lead cylinders is then designed to demonstrate the vibration suppression at subwavelength scales in two separate frequency regions, where the first-order outward hierarchy is selected. Good agreement between experimental and numerical results are clearly observed in the frequency response functions of a metamaterial sample. The hierarchical metamaterials are demonstrated to be efficiency solutions in elastic wave bandgap engineering at subwavelength scales, which will benefit light-weight passive structures for low-frequency vibration and/or elastic wave mitigation.