Rayleigh wave propagation in nonlinear metasurfaces

TL;DR

This paper explores how nonlinear effects in metasurfaces influence Rayleigh wave dispersion, revealing tunable filtering properties and spectral gap modifications through analytical and numerical methods.

Contribution

It introduces a closed-form analytical model for nonlinear Rayleigh wave dispersion in metasurfaces, highlighting the effects of nonlinearity type and energy loss on wave filtering.

Findings

Hardening nonlinearity reduces and can eliminate the filtering bandwidth.

Softening nonlinearity broadens spectral gaps at low strength and closes them at high strength.

Nonlinearity and energy loss together significantly alter dispersive properties.

Abstract

We investigate the propagation of Rayleigh waves in a half-space coupled to a nonlinear metasurface. The metasurface consists of an array of nonlinear oscillators attached to the free surface of a homogeneous substrate. We describe, analytically and numerically, the effects of nonlinear interaction force and energy loss on the dispersion of Rayleigh waves. We develop closed-form expressions to predict the dispersive characteristics of nonlinear Rayleigh waves by adopting a leading-order effective medium description. In particular, we demonstrate how hardening nonlinearity reduces and eventually eliminates the linear filtering bandwidth of the metasurface. Softening nonlinearity, in contrast, induces lower and broader spectral gaps for weak to moderate strengths of nonlinearity, and narrows and eventually closes the gaps at high strengths of nonlinearity. We also observe the emergence of a spatial gap (in wavenumber) in the in-phase branch of the dispersion curves for softening nonlinearity. Finally, we investigate the interplay between nonlinearity and energy loss and discuss their combined effects on the dispersive properties of the metasurface. Our analytical results, supported by finite element simulations, demonstrate the mechanisms for achieving tunable dispersion characteristics in nonlinear metasurfaces.