A nonlinear seismic metamaterial lying on layered soils

•A nonlinear seismic metamaterial lying on layered soils is proposed for Rayleigh wave attenuation.•An analytical model is developed to derive the dispersion and a FE simulation is conducted for validation.•The layer of clay decreases the phase velocity of Rayleigh wave and causes the linear bandgap to be compressed.•The softening nonlinear bandgap moves down and becomes narrower as the motion amplitude of the substrate increases. To protect engineering structures from being destroyed by earthquakes, seismic metamaterials have been proposed for Rayleigh wave attenuation. Introducing nonlinearity may provide new design options for seismic metamaterials. Although nonlinear seismic metamaterials lying on homogeneous substrates have been reported, the real stratigraphy is a layered structure. In the present work, Rayleigh wave propagation through a nonlinear seismic metamaterial is studied. The seismic metamaterial consists of nonlinear resonators attaching on layered soils composed of clayey slit and sandy slit. First, an analytical model is established, and the closed-form solution for the dispersion of nonlinear Rayleigh wave is calculated via the leading-order harmonic balance approach. Then, finite element (FE) simulations are conducted to obtain the wave mode, dispersion, as well as transmission, and validate the analytical results. This study shows that the clayey slit reduces the phase velocity of Rayleigh wave. Due to the interaction of the resonators with Rayleigh wave propagating in the layered substrate, solutions in the form of surface wave vanish within a certain frequency band. This frequency band is the bandgap for Rayleigh wave. The FE simulations further show that in this frequency band, the energy of Rayleigh wave is converted into bulk wave. Moreover, the dispersion of nonlinear Rayleigh wave is amplitude-dependent, which enhances the designability of seismic metamaterials.