Rayleigh waves guided by elastic metasurfaces coupled to a resonant half-space

Controlling the propagation of surface Rayleigh waves along complex geometries is essential for advanced engineering applications, including seismic wave mitigation, ultrasonic nondestructive testing, and surface acoustic wave technologies. However, energy leakage and scattering remain significant obstacles for this purpose. This paper discusses how resonant metamaterials can be used to guide Rayleigh waves along a non-flat irregular surface while minimizing scattering and energy loss in the bulk. This objective is achieved by designing an elastic metasurface of mass–spring oscillators, coupled to a resonant half-space constructed from several rows of periodically embedded mechanical resonators. In this framework, the metasurface is treated as a resonant boundary condition, whereas the resonant half-space is modeled as an equivalent homogenized medium characterized by effective mechanical parameters thanks to a dedicated homogenization technique. The sub-wavelength dimension for both surface and embedded resonators allows the derivation of a closed-form dispersion law. The dispersion analysis reveals the hybridization of the fundamental surface mode around the resonance frequency of the half-space, leading to the formation of a low-frequency bandgap. When the resonance frequency of the metasurface is tuned to fall within the bandgap frequency range, a highly confined and slow-moving surface mode emerges. This mode enables effective guidance of Rayleigh waves along surfaces with complex and irregular geometries. By tailoring the metasurface design, surface wave transmission can be optimized, while issues such as leakage and scattering at discontinuities are mitigated. This approach advances surface wave manipulation, offering promising implications for a wide range of engineering applications.