Abstract
In metamaterial science local resonance and hybridization are key phenomena strongly influencing the dispersion properties; the metasurface discussed in this article created by a cluster of resonators, subwavelength rods, atop an elastic surface being an exemplar with these features. On this metasurface, band-gaps, slow or fast waves, negative refraction and dynamic anisotropy can all be observed by exploring frequencies and wavenumbers from the Floquet-Bloch problem and by using the Brillouin zone. These extreme characteristics, when appropriately engineered, can be used to design and control the propagation of elastic waves along the metasurface. For the exemplar we consider, two parameters are easily tuned: rod height and cluster periodicity. The height is directly related to the band-gap frequency, and hence to the slow and fast waves, while the periodicity is related to the appearance of dynamic anisotropy. Playing with these two parameters generates a gallery of metasurface designs to control the propagation of both flexural waves in plates and surface Rayleigh waves for half-spaces. Scalability with respect to the frequency and wavelength of the governing physical laws allows the application of these concepts in very different fields and over a wide range of lengthscales.
Highlights
Recent years have witnessed the increasing popularity of metamaterial concepts, based on the so-called local resonance phenomenon, to control the propagation of electromagnetic (Pendry et al, 1999; Smith et al, 2004b; Ramakrishna and Grzegorczyk, 2008; Werner, 2016), acoustic, and elastic (Liu et al, 2000; Craster and Guenneau, 2012) waves in artificially engineered media
Attention focused on the existence of subwavelength band-gaps generated by the resonators (Pendry et al, 1998; Movchan and Guenneau, 2004; Achaoui et al, 2011; Lemoult et al, 2011; Colombi et al, 2014), and resulting frequency-dependent effective material parameters for negative refraction and focusing effects (Pendry, 2000; Smith et al, 2000; Yang et al, 2002; Li and Chan, 2004), and consideration is transitioning to methods for achieving more complete forms of wave control by encompassing tailored graded designs to obtain spatially varying refraction index (Pendry et al, 2006), wide band-gaps and mode conversion
If we limit our discussion to elastic metamaterials, potential applications could be implemented at any lengthscale
Summary
Recent years have witnessed the increasing popularity of metamaterial concepts, based on the so-called local resonance phenomenon, to control the propagation of electromagnetic (Pendry et al, 1999; Smith et al, 2004b; Ramakrishna and Grzegorczyk, 2008; Werner, 2016), acoustic, and elastic (Liu et al, 2000; Craster and Guenneau, 2012) waves in artificially engineered media. In the field of acoustic imaging, the tailored control of hypersound (elastic waves at GHz frequencies), used for cell or other nano-compound imaging or energy conversion and harvesting (Davis and Hussein, 2014; Della Picca et al, 2016), is emerging as one of the most promising applications of energy trapping and signal enhancement through metamaterials At this small scale, novel nanofabrication techniques deliver the tailoring possibilities required for graded devices (e.g., Alonso-Redondo et al, 2015; Rey et al, 2016). The high-frequency homogenization theory (Craster et al, 2010) establishes a correspondence between anomalous features of dispersion curves on band diagrams with effective tensors in governing wave equations: flat band and inflection (or saddle) points lead to extremely anisotropic and indefinite effective tensors, respectively, that change the nature of the wave equations (elliptic partial differential equations can turn parabolic or hyperbolic depending upon effective tensors) This makes analysis of dynamic anisotropy a potentially impactful work. The results (Figures 1 and 2) are presented using state of the art 2D or 3D time domain spectral element simulations (SPECFEM2D/3D, for an extensive introduction (Komatitsch and Martin, 2007; Peter et al, 2011; Rietmann et al, 2012)), while dispersion curves have been computed analytically for 1D cells (Figure 1), or via COMSOL Multiphysics for 2D elementary cells (Figures 3 and 4)
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