Exploring wave propagation in heterogeneous metastructures using the relaxed micromorphic model

Abstract

Metamaterials are artificial structures that can manipulate and control sound waves in ways not possible with conventional materials. While much effort has been undertaken to widen the bandgaps produced by these materials through design of heterogeneities within unit cells, comparatively little work has considered the effect of engineering heterogeneities at the structural scale by combining different types of unit cells. In this paper, we use the relaxed micromorphic model to study wave propagation in heterogeneous metastructures composed of different unit cells. We first establish the efficacy of the relaxed micromorphic model for capturing the salient characteristics of dispersive wave propagation through comparisons with direct numerical simulations for two classes of metamaterial unit cells: namely phononic crystals and locally resonant metamaterials. We then use this model to demonstrate how spatially arranging multiple unit cells into metastructures can lead to tailored and unique properties such as spatially-dependent broadband wave attenuation, rainbow trapping, and pulse shaping. In the case of the broadband wave attenuation application, we show that by building layered metastructures from different metamaterial unit cells, we can slow down or stop wave packets in an enlarged frequency range, while letting other frequencies through. In the case of the rainbow-trapping application, we show that spatial arrangements of different unit cells can be designed to progressively slow down and eventually stop waves with different frequencies at different spatial locations. Finally, in the case of the pulse-shaping application, our results show that heterogeneous metastructures can be designed to tailor the spatial profile of a propagating wave packet. Collectively, these results show the versatility of the relaxed micromorphic model for effectively and accurately simulating wave propagation in heterogeneous metastructures, and how this model can be used to design heterogeneous metastructures with tailored wave propagation functionalities.