Hybrid Rayleigh wave along a nonlocal nonlinear metasurface with two-degree-of-freedom spring-mass resonators

Abstract

Metasurfaces are devices employing the notion of resonance to transform seismic surface waves into body waves, thereby protecting the subwavelength structures. Using metasurfaces to control surface waves is a rapidly expanding field with intrinsic theoretical value and potential applications everywhere. In this paper, we have combined the concepts of nonlinearity, double mass system, and nonlocal elasticity to unveil the dispersive properties of hybrid Rayleigh waves. To enable a more compact construction for multi-frequency attenuation, two spring-mass resonators coupled with a nonlinear spring are used instead of single-mass resonators. A novel metasurface consisting of an array of nonlinear two-degree-of-freedom (two-mass) spring-mass systems is explored. This metasurface is connected to a nonlocal elastic substrate through a linear elastic spring. The paper provides a simple but effective analytical approach to study the dispersive properties of seismic metasurfaces. The complete explicit solutions are derived for the displacement of spring-mass systems and the Rayleigh waves in the nonlocal host substrate. Two frequency bandgaps are formed due to the presence of a dual spring-mass system in the metasurface. An attempt is made to explain the existence of these multi-frequency bandgaps as a result of the presence of multi-resonators. The effects of nonlinearities (softening and hardening) of the springs, nonlocal elasticity and relative amplitude inputs of the spring-mass system on the frequency (spectral) bandgaps are analyzed in detail via numerous plots.