An efficient model for seismic metasurfaces mitigating railway induced vibration

Locally resonant seismic metamaterials are emerging as an attractive ground vibration mitigation concept for vibration mitigation in the built environment. They consist of a subwavelength distribution of resonators on the ground surface or embedded in the soil. Resonator arrays of limited size, e.g. for isolating against railway induced vibration, can be modelled in full detail using finite elements (FE) coupled with boundary elements (BE). Soil displacements are evaluated as the superposition of an incident vibration and wave fields scattered by all resonators. Evaluating detailed multiple scattering between resonators with 3D geometries is computationally demanding, limiting the applicability of the method, especially in view of design optimization. A common simplification treats the resonator footprint as a point, allowing the use of analytical Green’s functions. Although highly efficient, this approach becomes inaccurate when the footprint size is not negligible with respect to the wavelength. In this paper, we investigate how relaxing through-soil interactions affects the multiple scattering between resonators with non-negligible footprint sizes and 3D geometries. Transfer functions from a rigid surface foundation, modelled using a 3D BE model, to points at the surface representing resonator positions are used. Complex resonator configurations are modelled using impedance matrices that relate the forces transmitted at the soil-structure interface to the participating mass in the translational and rotational motion. The proposed method is validated considering different wavelength-footprint ratios. An excellent correspondence is observed (1 - 80 Hz) with the solution from a 3D FE-BE model, with a significant (roughly 800 times) reduction in computational cost.