A seismic metamaterial: The resonant metawedge

Abstract

Critical concepts from three different fields, elasticity, plasmonics and metamaterials, are brought together to design a metasurface at the geophysical scale, the resonant metawedge, to control seismic Rayleigh waves. Made of spatially graded vertical subwavelength resonators on an elastic substrate, the metawedge can either mode convert incident surface Rayleigh waves into bulk elastic shear waves or reflect the Rayleigh waves creating a “seismic rainbow” effect analogous to the optical rainbow for electromagnetic metasurfaces. Time-domain spectral element simulations demonstrate the broadband efficacy of the metawedge in mode conversion while an analytical model is developed to accurately describe and predict the seismic rainbow effect; allowing the metawedge to be designed without the need for extensive parametric studies and simulations. The efficiency of the resonant metawedge shows that large-scale mechanical metamaterials are feasible, will have application, and that the time is ripe for considering many optical devices in the seismic and geophysical context.

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

“…Gudra & Stawiski (2000). Another recent application is associated with cloaking of surface waves and seismic metamaterials, see Brulé et al (2014) and Colombi et al (2016).…”

Elastic Wave Control Beyond Band-Gaps: Shaping the Flow of Waves in Plates and Half-Spaces with Subwavelength Resonant Rods

“…As already anticipated in Figure 1B, the first snapshot shows the band-gap (here the field is filtered between 0.35 and 0.4 MHz) produced by an array of resonators of constant height. In Figure 2E, we show the well-known phenomena of rainbow trapping (Tsakmakidis et al, 2007;Romero-Garcia et al, 2013; Zhu et al, 2013) for elastic waves (Colombi et al, 2016a). The combined graded and resonant structure allows the incoming Rayleigh waves to be slowed down selectively at different propagation distances inside the metasurface, and eventually to be trapped in a subwavelength area.…”

“…For this reason, 2D simulations in the P − SV plane (plane strain) are now shown. Technical details on how these simulations have been implemented can be found in previous studies (Peter et al, 2011;Colombi et al, 2015Colombi et al, , 2016a. As already anticipated in Figure 1B, the first snapshot shows the band-gap (here the field is filtered between 0.35 and 0.4 MHz) produced by an array of resonators of constant height.…”

“…The presence of these bandgaps have inspired the development of seismic metamaterials for Rayleigh waves (Colombi et al, 2016c) where the close relationship between shear S-and Rayleigh waves in the half-space lead to unexpected wave phenomena in the metamaterial. As chiefly demonstrated in Colombi et al (2016a) and Colquitt et al (2017), the resonance creates a hybrid branch bridging the Rayleigh line with the S-wave line. Through a graded resonators design (e.g., decreasing or increasing rod's height), the conversion becomes ultra-broadband, a key requirement for practical engineering applications.…”

“…When the wedge orientation is reversed, as in Figure 2F, the surprising phenomenon of modal conversion is obtained and the graded profile enhances the conversion on a large frequency band; in the previous section, this was already anticipated from the analysis of the dispersion curves. An alternative but straightforward description of trapping and conversion can be derived by plotting the dispersion curves as a function of the resonator length versus frequency as demonstrated in Colombi et al (2016a). The control possibilities emerging from this discussion suggest tremendous potential for applications of these metamaterials toward vibration reduction and enhanced sensing.…”