Architected materials that control elastic wave propagation are essential in vibration mitigation and sound attenuation. Phononic crystals and acoustic metamaterials use band-gap engineering to forbid certain frequencies from propagating through a material. However, existing solutions are limited in the low-frequency regimes and in their bandwidth of operation because they require impractical sizes and masses. Here, we present a class of materials (labeled elastic metastructures) that supports the formation of wide and low-frequency band gaps, while simultaneously reducing their global mass. To achieve these properties, the metastructures combine local resonances with structural modes of a periodic architected lattice. Whereas the band gaps in these metastructures are induced by Bragg scattering mechanisms, their key feature is that the band-gap size and frequency range can be controlled and broadened through local resonances, which are linked to changes in the lattice geometry. We demonstrate these principles experimentally, using advanced additive manufacturing methods, and inform our designs using finite-element simulations. This design strategy has a broad range of applications, including control of structural vibrations, noise, and shock mitigation. A rchitected materials exploit the geometry of their structure, which can be directly designed, to attain properties not common in bulk, continuum media. The underlying principles that determine the dynamic properties of architected materials are applicable across several length scales, and can be used to control phonons or elastic and acoustic waves, as in phononic crystals and acoustic metamaterials. In the linear regime, decreasing the size of the geometrical feature designed in the structure increases the operational frequency. This opens opportunities to control elastic/acoustic waves ranging from seismic excitations (hertz), structural vibrations (kilohertz), ultrasonic waves in microelectromechanical systems (MEMS) devices (megahertz), and thermal phonons in, e.g., thermoelectric materials (terahertz) (1-3).Advanced manufacturing techniques, such as 3D printing, have progressed over size scales, ranging from meters down to nanometers. With these techniques, complex structures can be realized in many materials such as polymers, metals, and ceramics. Here, we design and test 3D-printed, composite materials, which combine a polymeric matrix with metallic components, and present a previously unidentified type of architected materials for broadband vibration mitigation.Phononic crystals (PCs) consist of periodic arrangements of materials or components with controlled spatial sizes and elastic properties. When excited by an acoustic or elastic wave, PCs exhibit band gaps, or ranges of frequencies that cannot propagate through their bulk and decay exponentially. The band gaps in PCs arise from Bragg scattering mechanisms, and can be quite wide, making them desirable in sound mitigation and vibration absorption applications (4-8). However, the periodicity dimensi...

Resonant metamaterials have been proposed to reflect or redirect elastic waves at different length scales, ranging from thermal vibrations to seismic excitation. However, for seismic excitation, where energy is mostly carried by surface waves, energy reflection and redirection might lead to harming surrounding regions. Here, we propose a seismic metabarrier able to convert seismic Rayleigh waves into shear bulk waves that propagate away from the soil surface. The metabarrier is realized by burying sub-wavelength resonant structures under the soil surface. Each resonant structure consists of a cylindrical mass suspended by elastomeric springs within a concrete case and can be tuned to the resonance frequency of interest. The design allows controlling seismic waves with wavelengths from 10-to-100 m with meter-sized resonant structures. We develop an analytical model based on effective medium theory able to capture the mode conversion mechanism. The model is used to guide the design of metabarriers for varying soil conditions and validated using finite-element simulations. We investigate the shielding performance of a metabarrier in a scaled experimental model and demonstrate that surface ground motion can be reduced up to 50% in frequency regions below 10 Hz, relevant for the protection of buildings and civil infrastructures.

Discrete models provide concise descriptions of complex physical phenomena, such as negative refraction, topological insulators, and Anderson localization. While there are multiple tools to obtain discrete models that demonstrate particular phenomena, it remains a challenge to find metamaterial designs that replicate the behavior of desired nontrivial discrete models. Here we solve this problem by introducing a new class of metamaterial, which we term "perturbative metamaterial", consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model (individual masses and springs) to individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing 2D mechanical metamaterials that realize Veselago lenses, zero-dispersion bands, and topological insulators. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal, and photonic metamaterials composed of weakly interacting unit cells.

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We investigate the interaction of guided surface acoustic modes (GSAMs) in unconsolidated granular media with a metasurface, consisting of an array of vertical oscillators. We experimentally observe the hybridization of the lowest-order GSAM at the metasurface resonance, and note the absence of mode delocalization found in homogeneous media. Our numerical studies reveal how the stiffness gradient induced by gravity in granular media causes a down-conversion of all the higher-order GSAMs, which preserves the acoustic energy confinement. We anticipate these findings to have implications in the design of seismic-wave protection devices in stratified soils.

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