Gradient-based optimization of multi-modal seismic metasurfaces for broadband mitigation of environmental ground vibration

Mitigating vibration induced by railway traffic is challenging due to the need for effective reduction over a wide frequency range between 1 and 80 Hz. This paper presents a gradient-based optimization method to enhance the performance of seismic metasurfaces for the mitigation of railway induced vibration. The considered metasurface consists of an array of chiral resonators placed next to a railway track on the surface of the soil. Each resonator consists of two mass elements connected by slender ligaments. This type of resonator has been chosen because its geometry induces coupled axial–rotational motion, increasing the effective inertia and improving attenuation performance at low frequencies. The displacement field resulting from a passing train is calculated using a combination of 2.5D and 3D coupled finite element–boundary element methods. The expected power flow through an auxiliary plane behind the metasurface is computed as a global metric of the metasurface’s effectiveness. The cross section of the ligaments and the thickness of the masses of the chiral resonators are optimized using a gradient-based method, minimizing the integrated power flow over a range of frequencies. An adjoint formulation is developed to efficiently compute gradients. This study assesses the performance of the metasurface during the passage of a four-car EMU train on a ballasted track on layered soil. The performance of the optimized metasurface is benchmarked against a graded configuration with the same total mass, obtained by linearly varying the ligament cross section. The results illustrate the benefits of tuning the properties of the metasurface to the particular characteristics of a case history.