Resonant topological metasurface for Rayleigh wave attenuation and energy localization in homogeneous and layered elastic half-spaces

Abstract

In this work, we design a resonant topological metasurface based on the Su-Schrieffer-Heeger model and investigate its energy localization and interaction with Rayleigh waves in both homogeneous and layered elastic half-spaces. To this aim, we establish a general analytical framework using the thin-layer method and multiple scattering theory. This approach allows us to calculate the spatially modulated frequency spectrum, revealing the presence of a topologically nontrivial bandgap (TNBG). Also, eigenfield and flux analyses capture a topologically protected interface mode (TPIM) at the interface between two domains with distinct topological unit cells. Further wave field analysis shows that the TPIM enables significant Rayleigh wave energy localization. Meanwhile, the TNBG exhibits dual attenuation mechanisms of Rayleigh-to-Rayleigh Bragg backscattering and Rayleigh-to-bulk wave conversion, demonstrating a strong wave attenuation capability. In addition, the topological metasurface displays robust performance against half-space stratification, as its topological properties remain unaffected by higher-order Rayleigh modes. It maintains great energy localization and excellent vibration mitigation performance in the layered elastic half-space. This resonant topological metasurface provides a promising new approach for low-frequency Rayleigh wave mitigation and energy harvesting in real foundations.