Zero-energy topological oppy edge modes have been demonstrated in families of kagome lattices with geometries that differ from the regular case composed of equilateral triangles. In this work, we explore the behavior of these systems in the limit of continuum elasticity, which is established when the ideal hinges that appear in the idealized models are replaced by ligaments capable of supporting bending deformation, as observed in realistic physical lattices. Under these assumptions, the oppy edge modes are preserved but shifted to finite frequencies, where they spectrally overlap with the acoustic bulk modes. The net result is the establishment of a relatively broad low-frequency regime over which the lattices display strong asymmetric wave transport capabilities. By simply varying the thickness of the ligament of the unit cell, we can obtain a variety of lattices with different localization capabilities. Through theoretical analysis and finite element simulations, we parametrically explore the localization capabilities of different configurations, thus establishing a qualitative relation between the topological descriptors of the unit cell and the effective global transmission properties of the lattice. Using simple elasticity arguments, we provide a mechanistic rationale for the observed range of behaviors. Our study has implications for the design of mechanical filters, structural logic components, and acoustic metamaterials for wave manipulation at large.
One of the most daunting limitations of phononic crystals and acoustic/elastic metamaterials is their passivity: a given configuration is bound to display its phononic properties only around its design point, i.e., working at some pre-determined operating conditions. In the past decade, this shortcoming has inspired the design of phononic media with tunable wave characteristics; noteworthy results have been obtained through a family of methodologies involving shunted piezoelectric elements. Shunting a piezoelectric element means connecting it to a passive electric circuit; tunability stems from the ability to modify the effective mechanical properties of the piezoelectric medium by modifying the circuit characteristics. One of the most popular shunting circuits is the resistor-inductor, which allows the patch-and-shunt system to behave as an electromechanical resonator. A common motif among the works employing shunted piezos for phononic control is periodicity: the patches are typically periodically placed in the domain and the circuits are identically tuned. The objective of this work is to demonstrate that the wave attenuation performance of structures with shunted piezoelectric patches can be improved by leveraging notions of organized disorder. Based on the idea of rainbow trapping broadband wave attenuation obtained by tuning an array of resonators at distinct neighboring frequencies we design and test an electromechanical waveguide structure capable of attenuating waves over broad frequency ranges. In order to emphasize the fact that periodicity is not a binding requirement when working with RL shunts (which induce locally resonant bandgaps), we report on the performance of random arrangements of patches. In an attempt to demonstrate the tunability attribute of our strategy, we take advantage of the reconfigurability of the circuits to show how a single waveguide can attenuate both waves and vibrations over different frequency ranges.
Phononic crystals (PCs) are periodic media known for their spectral and spatial wave manipulation capabilities, among which we recall their stop-band filtering behavior, due to the formation of phononic bandgaps, and the spatial directivity, i.e., the inherent ability to produce directional wave patterns. In general, the anisotropic wave propagation patterns of PCs are characterized by multiple equipotent directions of wave beaming, a characteristic which prevents the effective de-energization of arbitrarily selected regions of the PC domain. In this work we discuss a few enhancements of the directivity of lattice-like PCs, obtained through the introduction of shunted piezoelectric inclusions. The lattice links of each unit cell are instrumented with piezoelectric patches, each connected to a separate negative capacitance circuit. By properly choosing the shunting parameters for selected subsets of patches, we can generate peculiar anisotropic stiffness landscapes and reconfigure the elastic wave patterns accordingly.
KEYWORDS: Data modeling, Wave propagation, Diagnostics, Data acquisition, Principal component analysis, Inspection, Nondestructive evaluation, Scattering, Velocity measurements, Data processing
This work investigates the problem of anomaly detection by means of an agnostic inference strategy based on the concepts of spatial saliency and data sparsity. Specifically, it addresses the implementation and experimental validation aspects of a salient feature extraction methodology that was recently proposed for laser-based diagnostics and leverages the wavefield spatial reconstruction capability offered by scanning laser vibrometers. The methodology consists of two steps. The first is a spatiotemporal windowing strategy designed to partition the structural domain in small sub-domains and replicate impinging wave conditions at each location. The second is the construction of a low-rank-plus-outlier model of the regional data set using principal component analysis. Regions are labeled salient when their behavior does not belong to a common low-dimensional subspace that successfully describes the typical behavior of the anomaly-free portion of the surrounding medium. The most at tractive feature of this method is that it requires virtually no knowledge of the structural and material properties of the medium. This property makes it a powerful diagnostic tool for the inspection of media with pronounced heterogeneity or with unknown or unreliable material property distributions, e.g., as a result of severe material degradation over large portions of their domain.
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