Rayleigh wave propagation in nonlinear metasurfaces

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