Lightweight self-similar hierarchical metamaterials with subwavelength and superwide bandgaps

Abstract

Vibration isolation has always been a flourishing subject with practical interest because it helps in reducing structure vibration that has serious effects on moving vehicles and equipment operation, and it exists everywhere and incessantly in daily life. With the advantage of predictable and designable frequency bandgaps, elastic metamaterial has attracted a lot of research attention in the past decade and beyond. Inspired by the design of Chinese traditional window and kirigami pattern, this paper introduces a self-similar hierarchical elastic metamaterial that can offer superwide subwavelength bandgaps without increasing system weight. The comparison of band structures obtained by finite element simulation manifests significant effects of hierarchy design on lowering bandgap frequency and widening bandgap width. Through comprehensive analyses, the principles for maximizing bandgap width without increasing system weight are highlighted. The vibration response of supercells that consist of 2 × 3 unitcells is constructed for both the first- and second-order hierarchical structures are investigated. After analyzing the different working frequencies of supercells with distinct hierarchical ratios, the first-order and second-order hybrid hierarchical supercells containing unitcells with complementary bandgaps are designed. An excellent increase in effective and perfect attenuation width is demonstrated. The work presented herein provides a new and effective method for generating subwavelength and superwide bandgaps in lightweight structures. This advancement holds great promise for improving the application potential of elastic metamaterials.