Efficient modelling and design of multimodal seismic metasurfaces for broadband ground vibration mitigation

  • Carneiro, David (KU Leuven)
  • Giannini, Daniele (KU Leuven)
  • François, Stijn (KU Leuven)
  • Lombaert, Geert (KU Leuven)
  • Degrande, Geert (KU Leuven)

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Inspired by promising results obtained with seismic metamaterials to protect civil structures, we investigate how seismic metamaterials can mitigate railway induced vibration (1 - 80 Hz). This is a very challenging problem, as the wide spectrum of railway induced vibration requires broadband mitigation. Moreover, a complex vibration pattern is created during a train passage due to the omnidirectional wave radiation from each axle of the train exciting a large volume of soil, as well as multiple wave reflections and refractions at the layer interfaces of a stratified soil. A 3D finite element - boundary element (FE-BE) formulation can be used for modelling the soil-metasurface interaction. Evaluating detailed interaction between a large number of resonators involves substantial computational time and memory, limiting the applicability of the method. An efficient relaxed approach is therefore proposed under the assumption that the wavelengths of interest are much longer than the dimensions of the soil-resonator interface. Transfer functions from a single rigid foundation to single points at the surface representing resonator positions can therefore be used. The proposed method is verified considering different wavelength-footprint ratios. An excellent accuracy and a significant (roughly 2800 times) reduction in computational time is obtained, offering an accurate and efficient solution to problems involving a large number of resonators. The effectiveness of resonator arrays composed of mass-spring systems is widely studied. They have limited effectiveness as only their vertical motion affects surface waves. In this work, multimodal metasurfaces are proposed. A resonator consisting of plates connected by ligaments with opposite chirality is employed. This design induces coupled torsional-vertical modes, enhancing performance. The effectiveness of chiral resonators on a homogeneous soil is investigated. Mitigation between 20 and 80 Hz is obtained using a graded configuration. The results stimulate using this new concept to protect civil structures from ground vibration.