This thesis studies the use of metamaterials for mitigating train-induced ground-borne vibrations, a growing issue with the projected increase in train transportation. Traditional mitigation measures such as trenches often fall short, particularly at low frequencies and small incidence angles. Metamaterials, engineered to alter wave propagation properties, offer a novel solution by creating frequency bands that attenuate vibrations. This study begins with an one-dimensional model of an Euler-Bernoulli beam on a visco-elastic foundation, where metamaterials are modeled as local mass-spring-dash pots and single-degree-of-freedom resonators. This model facilitates an analytical study into wave propagation and band gap formation using Floquet analysis, which identified band gaps arising from both local resonances and the periodicity of resonator arrangements.

The study progresses by examining a finite periodic system using a numerical model. This involves comparing the dispersive properties of the finite system with those observed in its infinite counterpart. The results demonstrate an excellent agreement between the two. A significant focus is on the "metawedge", a metamaterial configuration with unit cells varying in natural frequency, allowing for broadband frequency targeting. This configuration enables elastic rainbow trapping and wave-mode conversion, with detailed three-dimensional analysis performed using FEMIX to explore these phenomena further. The three-dimensional model consists out of a homogeneous elastic half-space with single-degree-of-freedom resonators placed on top of the surface. The results demonstrate that the proposed metamaterial solutions are effective in mitigating low-frequency vibrations caused by trains across all incidence angles. The findings indicate that the classic metawedge configuration traps waves, by slowing them down, while the inverse metawedge accelerates waves, facilitating wave-mode conversion.