Bandgap Characteristics And Dynamic Behaviours Of Mechanical Metamaterials

Abstract

This study’s aim is to systemically demonstrate the bandgap characteristic and dynamic performance of mechanical metamaterials and attempt to evaluate the relationship between them, based on theoretical models, finite element analyses and experimental investigations. This study starts with the design and comprehensive investigation of a 1D metamaterial chain with a dual resonance system. The modified mass-spring analogy and the effective property theory successfully predict the bandgap characteristics and the wave attenuation capacity of the proposed metamaterial. Subsequently, by hybridizing the negative Poisson’s ratio property and the local resonant mechanism, a novel 2D mechanical metamaterial is proposed by embedding metal inclusions as resonators into a conventional reentrant frame, forming a hybrid metamaterial (HMM). By controlling the ratio of the bandgap width to the frequency band width of impact excitations, i.e., the bandgap overlap ratio, an attempt is made to quantify the relationship between the bandgap characteristics and the dynamic performance of HMM under impact load. With the aim of improving the impact mitigation performance and simultaneously reducing the total weight of the proposed HMM, two configurations, i.e., graded-type and dual-type metamaterials, are designed and developed to superpose the bandgap of each layer and induce the coupling effect in local resonant mechanisms, respectively. Additionally, the Continuous Wavelet Transform method is utilised to evaluate the dynamic performance of different local unit cells by determining time-frequency-locations details. Finally, the proposed HMM is extended to 3D structures, following the abovementioned design principles. With the help of vibration mode analyses near the edge frequency of bandgaps, a study on the design flexibility of 3D-HMM reveals the sensitivity of the key geometrical parameters on the material properties and the bandgap characteristics.