Waveguiding Rayleigh waves along non-flat surfaces via locally resonant metamaterials

This study presents a strategy for guiding surface Rayleigh waves along non-flat, irregular surfaces with minimal energy leakage and scattering. The objective is achieved by designing an elastic metasurface composed of discrete mass-spring oscillators, coupled to a resonant half-space made of several rows of periodically embedded mechanical resonators. The subwavelength dimensions of both surface and embedded resonators enable the derivation of a closed-form dispersion relation. In this framework, the metasurface is modeled as a dynamic boundary condition, while the resonant half-space is represented as an equivalent homogenized medium characterized by effective mechanical parameters through a dedicated homogenization technique. The key findings reveal the hybridization of the fundamental surface mode around the resonance frequency of the resonant half-space, leading to the formation of a low-frequency bandgap. When the metasurface is designed with a resonance frequency lying within this bandgap frequency range, a highly confined and slow-propagating surface mode emerges. This mode enables efficient guidance of surface waves along irregular geometries, minimizing energy loss while maintaining strong wave localization [1]. The results are validated through full-field finite element simulations. This work contributes to the development of innovative approaches for surface wave manipulation in engineering and technological applications, including ground-borne vibration mitigation systems. REFERENCE: [1] Zeighami, F., Palermo, A., Shokouhi, P., & Marzani, A. (2026). Rayleigh waves guided by elastic metasurfaces coupled to a resonant half-space. Journal of Sound and Vibration, 621, 119482. doi:10.1016/j.jsv.2025.119482