Tailored elastic surface to body wave Umklapp conversion

Abstract

Elastic waves guided along surfaces dominate applications in geophysics, ultrasonic inspection, mechanical vibration, and surface acoustic wave devices; precise manipulation of surface Rayleigh waves and their coupling with polarised body waves presents a challenge that offers to unlock the flexibility in wave transport required for efficient energy harvesting and vibration mitigation devices. We design elastic metasurfaces, consisting of a graded array of rod resonators attached to an elastic substrate that, together with critical insight from Umklapp scattering in phonon-electron systems, allow us to leverage the transfer of crystal momentum; we mode-convert Rayleigh surface waves into bulk waves that form tunable beams. Experiments, theory and simulation verify that these tailored Umklapp mechanisms play a key role in coupling surface Rayleigh waves to reversed bulk shear and compressional waves independently, thereby creating passive self-phased arrays allowing for tunable redirection and wave focusing within the bulk medium.

Topological Rainbow Trapping for Elastic Energy Harvesting in Graded Su-Schrieffer-Heeger Systems

“…Similar to rainbow trapping devices [73,74], the metawedge achieves local-field enhancement, which can be used for energy-harvesting [42]. Despite the success, both in design and experimental verification, of a wide variety of effects exhibited by the metawedge and similar structures [39][40][41], this simplistic array has reflections, due to Bragg scattering, at the "trapping" positions. As such, energy is not confined for prolonged periods due to intermodal coupling, and rainbow reflection phenomena is seen instead [43].…”

“…Galvanized by the amplifications achieved by the 1D topological edge states in elastic beams, we now turn our focus to full three-dimensional (3D) (isotropic) elastic half-spaces, patterned with arrays of resonant rods on the surface. This structuration creates a so-called metawedge and these have been used to exhibit extraordinary control of surface Rayleigh waves in terms of rainbow devices and tailored surface to body wave converters [38,39,41]; here we explore graded-SSH structures for the elastic half-space. Elastic half-spaces support a wider variety of waves than the motivational KL plates or elastic beams.…”

“…Further to this, two polarizations of body waves, namely compressional (P) and vertical and horizontal shear (SV and SH) waves exist, both traveling at differing wave speeds c p and c s , respectively, such that c p > c s > c r [86]. Unlike recently designed mode-conversion devices [41], we focus here on exciting topologically protected surface waves by utilizing the now familiar SSH model of rods, but now placed atop such a half-space. Similar analysis of the dispersion curves of two structures S1 and S1 show the existence of an edge mode at the domain boundary between the two geometries, which are similar to those considered on the beam, but now with the rods atop a finite elastic halfspace, shown in Fig.…”

“…To further emphasize the utility of these devices, and to better emulate a true metawedge, we extend the device to include several rows of the graded-SSH geometry, representing those considered in Ref. [39,41]. This barrier configuration enables the excitation of more edgemodes in the perpendicular direction.…”

“…Despite their relative simplicity, 1D topological insulators serve not only as pedagogical examples, but possess useful features for applications ranging from lasing [33] to mechanical and acoustic transport [34][35][36]. Motivated by applications in elastic energy harvesting, we highlight a modality of 1D topological insulators, based on the wellestablished Su-Schrieffer-Heeger (SSH) model [37], via the amalgamation of this model with graded metawedge structures [38][39][40][41].…”