Abstract Summary
Although rail is a sustainable and climate-friendly means of transport, vibration remains a particular environmental concern as it may cause annoyance to people and disturbance of sensitive equipment. Inspired by promising results obtained with seismic metamaterials to protect civil infrastructure from earthquakes [1], we aim to investigate how seismic metamaterials can mitigate railway induced vibration in a wide frequency band (1 – 80 Hz). This can be accomplished by placing resonators on the transmission path between track and buildings [2,3]. Attenuating vibration induced by moving dynamic axle loads remains challenging. Furthermore, vibration reduction is required in a broad frequency range. The challenge is also aggravated by considering layered soils, in which vibration is mainly propagating as a superposition of dispersive surface waves. Detailed models based on 3D coupled finite element - boundary element (FE-BE) formulations are developed to analyze the effect of seismic metasurfaces on railway induced vibration in a broad frequency band. Fixed loads applied on the surface of the soil and moving loads are considered. The resonators are modeled as a single degree of freedom systems on top of square concrete foundations. The soil is represented as a homogeneous halfspace or a horizontally layered medium. A uniform metasurface consisting of identical resonators on a homogeneous halfspace is considered first. The wavenumber-frequency spectrum and transfer function show a clear narrow band gap around the resonance frequency of the oscillators. This band gap is widened over a broader range of frequencies (40 – 70 Hz) using so-called classical and inverse metawedges, evoking rainbow trapping or conversion of surface waves into bulk shear waves, respectively [4]. For layered soil conditions, a uniform metasurface creates a partial band gap where mainly the fundamental mode is affected. The transfer function at a receiver behind the metasurface shows a shift in frequency. At a single frequency, non-uniform attenuation is found behind the metasurface, in contrast to the uniform attenuation observed in a homogeneous halfspace. Vibration mitigation in a wide frequency band still emerges using metawedges. Their efficiency, however, is reduced and the surface-to-shear wave conversion evoked by inverse metawedges in homogeneous media is no longer observed. We are presently performing analyses for moving loads on layered media with seismic metasurfaces. [1] S. Brûlé, E.H. Javelaud, S. Enoch, and S. Guenneau. Experiments on seismic metamaterials: molding surface waves. Physical Review Letters, 112(13):133901, 2014. [2] A. Palermo, S. Krödel, K.H. Matlack, R. Zaccherini, V.K. Dertimanis, E.N. Chatzi, A. Marzani, and C. Daraio. Hybridization of guided surface acoustic modes in unconsolidated granular media by a resonant metasurface. Physical Review Applied, 8:054026, 2018. [3] P.-R. Wagner, V.K. Dertimanis, I.A. Antoniadis, and E.N. Chatzi. On the feasibility of structural metamaterials for seismic-induced vibration mitigation. International Journal of Earthquake and Impact Engineering, 1(1-2):20–56, 2016. [4] A. Colombi, D. Colquitt, P. Roux, S. Guenneau, and R.V. Craster. A seismic metamaterial: The resonant metawedge. Scientific Reports, 6:27717, 2016.
