Surface manipulation of elastic half-space to suppress Rayleigh wave propagation: A step towards boundary condition-based meta-surface design

Abstract

A boundary condition (BC)-based design methodology for metasurfaces was recently proposed to control low-frequency Lamb waves in a plate. This study highlights the significance of a type of Cauchy BCs, called Mindlin BCs, for controlling Rayleigh wave propagation and provides motivation for a BC-based metamaterial design for surface wave control. Analytical study on an elastic half-space with Mindlin BCs reveals no possible surface wave solutions. The frequency-domain and time-domain simulations by imposing Mindlin BCs on the surface in the path of Rayleigh wave propagation are consistent with analytical predictions exhibiting no surface wave transmission. The simulation results 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 Mindlin BC patch, a portion of mode-converted bulk waves near the surface converts back to Rayleigh waves at the end of the BC patch suggesting the requirement of a minimum Mindlin BC patch length for effective suppression of surface waves. Finally, we show that frequency-dependent Mindlin BCs are imposed by an array of rod-like resonators resulting in a surface wave bandgap. These findings provide new insights into designing novel metasurfaces that provide the necessary coupling for desired surface wave control.