Reflective metasurfaces with multiple elastic mode conversions for broadband underwater sound absorption

Abstract

Unlike their electromagnetic and acoustic counterparts, elastic waves involve different wave modes. The interplay and the coupling among them increase the complexity of the problem while also offering a larger space for wave manipulation. Elastic bulk wave conversion in an elastic metamaterial has recently shown great promise in medical ultrasound and nondestructive testing. Unlike the transmission-type conversion, however, reflective elastic mode conversion has been explored less in terms of analysis and design, despite the enormous possibilities that it might offer for energy trapping and dissipation. In this work, we develop a theoretical framework for constructing elastic anisotropic metasurfaces that can enable reflective longitudinal-to-transverse (L-to-T) and transverse-to-longitudinal (T-to-L) wave conversions. We capitalize on the mechanism of multiple reflective mode conversion to achieve broadband, subwavelength, and near perfect sound absorption in the underwater environment. The reflective scattering properties of the metasurfaces are systematically exploited for incident longitudinal or transverse waves. The conversion mechanism is rooted in reflective Fabry-Perot (FP) resonance, whose occurrence conditions and features are predicted for prescribed effective parameters of the metasurface. We then establish an inverse-design framework for conceiving an underwater coating system formed by a viscoelastic rubber layer and the metasurface. A series of metasurfaces allowing for customized mode conversions are realized for delivering broadband low-frequency and high-efficiency underwater sound absorption. Specifically, an ultrathin rubber-metasurface layer in which the metasurface with a thickness of approximately λ/70 can lead to nearly 100% sound absorption. Furthermore, we demonstrate that a persistently high absorption (over 80%) can be obtained in a rather robust manner within a wide range of wave incidence angle from −60° to 60°. More importantly, high-efficiency acoustic absorption exceeding 75% can be readily achieved through multiple mode conversions within the ultrabroadband range featuring a relative bandwidth of 119%. We reveal the combined FP resonance mechanism of underwater sound absorption, i.e., the FP resonance of the metaconverter, which determines the L-to-T and T-to-L conversion ratio, and the FP resonance of the rubber-metasurface layers, which enhances the wave attenuation inside the rubber. The proposed reflective multiple mode-conversion mechanism and metasurface design methodology open a route towards a class of elastic-wave-based devices with promising potential for underwater applications.