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...

This paper presents a comprehensive review of the current state of knowledge of second harmonic generation (SHG) measurements, a subset of nonlinear ultrasonic nondestructive evaluation techniques. These SHG techniques exploit the material nonlinearity of metals in order to measure the acoustic nonlinearity parameter, β. In these measurements, a second harmonic wave is generated from a propagating monochromatic elastic wave, due to the anharmonicity of the crystal lattice, as well as the presence of microstructural features such as dislocations and precipitates. This article provides a summary of models that relate the different microstructural contributions to β, and provides details of the different SHG measurement and analysis techniques available, focusing on longitudinal and Rayleigh wave methods. The main focus of this paper is a critical review of the literature that utilizes these SHG methods for the nondestructive evaluation of plasticity, fatigue, thermal aging, creep, and radiation damage in metals.

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.

Nonlinear ultrasound was used to monitor radiation damage in two reactor pressure vessel (RPV) steels. The microstructural changes associated with radiation damage include changes in dislocation density and the formation of precipitates, and nonlinear ultrasonic waves are known to be sensitive to such changes. Six samples each of two different RPV steels were previously irradiated in the Rheinsberg power reactor to two fluence levels, up to 10 20 n/cm 2 (E > 1 MeV). Longitudinal waves were used to measure the acoustic nonlinearity in these samples, and the results show a clear increase in the measured acoustic nonlinearity from the unirradiated state to the medium dose, and then a decrease from medium dose to high dose. V

Interaction of guided wave modes in isotropic weakly nonlinear elastic plates: Higher harmonic generationThis research experimentally characterizes the efficiency of Lamb wave mode pairs to generate the cumulative second harmonic in an undamaged aluminum plate. Previous research developed the theoretical framework for the characteristics of second harmonic generation of Lamb waves in nonlinear elastic plates, and identified five mode types where the amplitude of the measured second harmonic should increase linearly with ultrasonic wave propagation distance. The current research considers one of these five mode types, Lamb wave mode pairs at the longitudinal velocity, and experimentally confirms the theoretically predicted ratios of the rate of accumulation of the second harmonic amplitude versus propagation distance for two different Lamb wave mode pairs. By comparing these rates of accumulation, these experimental results are used to characterize the measurement efficiency of the mode pairs under consideration.

This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β11 is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β11(7075)/β11(2024) measure of 1.363 agrees well with previous literature and earlier work. The proposed work is also applied to a set of 2205 duplex stainless steel specimens that underwent various degrees of heat-treatment over 24h, and the results improve upon conclusions drawn from previous analysis.

Architected lattices can be designed to have tailorable functionalities by controlling their constitutive elements. However, little work has been devoted to comparing energy absorption properties in different periodic three-dimensional geometries to each other and to comparable foam-like random structures. This knowledge is essential for the entire design process. In this work, the authors conduct a systematic and comprehensive computational study of the quasi-static and dynamic energy absorption properties of various different geometries. They test compression loading over strain rates varying from 1 to 10 4 s −1 . The authors analyze geometries with varying degrees of nodal connectivity, ranging from bending dominated to stretching dominated, at different orientations, and compare their response to equivalent stochastic lattices. Results show relatively high stress peaks in the periodic lattices, even in bending dominated lattices at certain orientations. Conversely, the stochastic geometries show a relatively constant stress response over large strains, which is ideal for energy absorbing applications. Still, results show that specific orientations of bending dominated periodic lattice geometries outperform their stochastic equivalents. This work can help to quickly identify the potential of different unit cell types and aid in the development of lattices for impulse mitigation applications, such as in protective sports equipment, automotive crashworthiness, and packaging.

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.