Elastic Waves in Periodic and Locally Resonant Metamaterials:Algorithms for Fast Dispersion Computation and Applications for Seisimic Wave Isolation

Periodic and locally resonant materials, also referred as metamaterials, provide unique opportunities for elastic wave control across different length scales, ranging from thermal insulation at the nanoscale to meter-size devices for seismic attenuation. The properties of periodic/locally resonant media can be investigated at the unit cell level, which describes the full dynamics of the material. Unit cell modeling requires fast computational approaches which can capture the filtering properties of these materials. Additionally, when large scale applications for seismic wave attenuation are envisioned, the extra challenge is to design unit cells of feasible dimensions and practical implementation. Starting from these considerations, in this dissertation, two primary objectives are pursued within two distinct Parts of the thesis. In Part I, fast numerical approaches to extract the dispersive properties of periodic/locally resonant materials are investigated. In Part II, an innovative isolation device for seismic wave attenuation, named seismic metabarrier, is presented. In more detail, Part I presents two Finite Element based model reduction techniques: (i) the first one combines a Component Mode Synthesis (CMS) reduction and a Wave Finite Element approach to accurately extract the material complex dispersion with reduced computational time; (ii) the second one relies on a Wave-based model reduction technique applied on the CMS reduced model to further ease the band structure computational effort. Part II presents the seismic metabarrier, which consists of an array of local resonators buried at the soil surface to convert Rayleigh waves into shear bulk waves. Analytical, numerical and scaled experimental studies performed on the metabarrier show promising results for the attenuation of surface waves in the low-frequency regime. The required barrier dimensions to achieve a significant ground motion attenuation are evaluated with different parametric studies. Finally, the metabarrier design is optimized using multi-mass resonators which minimize the barrier dimensions for its practical implementation.