Steering of Acoustic Reflection from Metasurfaces through Numerical Optimization

Abstract

Space-coiling metamaterials that exploit the so-called generalized Snell's law are suitable for the subwavelength manipulation of acoustic waves, leading to extraordinary refracting and reflecting metasurfaces. Typically, space-coiling metasurfaces are characterized by a narrow operating range in frequency due to the intrinsic connection between the design wavelength and the characteristic dimensions of the metasurface. The main goal of the present work is to design a broadband and modular space-coiling based metasurface, extending the range of frequency where the effective metabehaviour is achieved. The metasurface building set is composed by eight different unit cells, each introducing a tailored phase shift in the field, that can be combined side by side to produce the desired acoustic effect. The design parameters of each cell are selected as the result of an optimization process that minimizes the dependency on the operating frequency of the metabehaviour, keeping the overall thickness below a quarter of the design wavelength. Significant results are obtained for benchmark problems.

A metacontinuum model for phase gradient metasurfaces

“…The HR and SC cells used have been designed through the optimization procedure described in 28 . Therefore, the design parameters were set to be the original ones from the cited work for the SC, expressed in terms of a, b, d, t, w or widths and heights of the necks and cavities for the HR ones, r n , r c , h n , h c as described in Fig.…”

“…However, some exceptions can be found in the literature 25 that exploit non-locality to enhance the device's performance. Thin devices with broadband effect 26,27 , also achieved with design by optimization 28,29 , received particular attention. Results have been obtained in the literature with cells of various shapes, such as straight tubes 27,30 , space-coiling cells 19,31,32 , spiral structures 22,26,33 , Helmholtz resonators 34,35 , or more complex microstructures 36,37 , modelling their effects using several approaches, such as equivalent refractive index 38 , equivalent impedance 19 , effective isotropic medium with equivalent density and speed of sound 36 One of the characteristics of metamaterials and metasurfaces is that their structure can be very complex also at a micro-level.…”

On the integration of acoustic phase-gradient metasurfaces in aeronautics

“…Previous researches show several practical ways to realize this effect, [4][5][6][7][8][9][10][11] achieving remarkable results in terms of subwavelength thickness and bandwidth of the devices. 12,13 However, if on one hand particular attention has been paid to the development of metasurfaces operating in media at rest, very little has been done to take into account convective effects. [13][14][15][16][17][18] The European project AERIALIST (AdvancEd aircRaft noIse AlLeviation devIceS using meTamaterials) aims at extending the theory of metamaterials and developing suitable numerical tools to take into account realistic aerodynamic flows.…”

“…The issue is hence moved to the possibility to find a design, or a combination of more, for the elementary cells capable to replicate that dynamic. This nontrivial task can be, for example, addressed again via optimization, as in Palma et al 12 Regardless of the method adopted, however, its success is not guaranteed apriori as it strongly depends on the specific design.…”