Control of Rayleigh wave propagation through imposing Mindlin boundary conditions on the surface

Abstract

A resonant metasurface design based on boundary condition (BC) manipulation was recently established to control low-frequency Lamb waves in a plate. This study identifies the necessary BCs that forbid Rayleigh wave propagation in order to find a rational design methodology for an optimized BC-controlled meta-surface. An analytical study of Mindlin BCs, a type of Cauchy BCs, shows promise in surface wave control. The frequency-domain and time-domain finite element studies performed by imposing Mindlin BCs in the path of Rayleigh wave propagation are consistent with analytical predictions, exhibiting no Rayleigh wave transmission. The simulations reveal mode conversions from Rayleigh wave to bulk waves directed into the half-space and a low amplitude Rayleigh wave reflection. For a finite-sized BC patch, the radial beam spreading of the mode-converted bulk waves keeps some energy near the surface, which could convert back to Rayleigh waves at the end of the BC patch. Thus, the BC patch must be sufficiently long to effectively suppress surface waves. Finally, we show that the Mindlin BCs can be imposed by a rod-like prismatic resonator at the resonator’s longitudinal frequency. These findings provide new insights into the coupling that promotes surface wave control, potentially leading to novel metasurface designs.