Modal-Based Analysis for Aiding 3D Elastic Metastructure Design

Abstract

The engineered topological structures of the unit cell endow elastic metamaterials (EMMs) with the extraordinary capability to attenuate elastic waves. In real-life scenarios, a practical EMM (i.e., metastructure), consisting of a limited number of unit cells, is the truncation of the infinite EMM, which may detriment seriously the attenuation capability. To understand the mechanism behind the detriment, an efficient way to evaluate and analyze the stopbands for metastructures is essential. Instead of relying on the commonly adopted frequency response analysis to characterize stopbands for metastructures, which are sensitive to frequency sweeping steps and short of information of truncated resonance affecting wave attenuation performance, a novel modal-based method (MM) is proposed to assess the wave attenuation of 3D metastructures. Specifically, the modal-based analysis scheme incorporating the modal superposition principle and a freshly developed layer-based strain energy ratio (SER) measurement method is proposed. Through employing the MM, the opening and ceasing of the stopbands are evaluated by characterizing dominant eigenmodes developed in metastructures. Accordingly, the influences of eigenmodes induced by different mechanisms on wave attenuation performance are investigated, and the stopband formation mechanisms are elaborated. Furthermore, under the guidance of a freshly proposed modal-based design framework, metastructures with modified geometrical parameter settings (GPSs) are demonstrated with enlarged normalized bandwidths (NBs) at lower frequencies, which show improved applicability in multiple engineering disciplines.