Design and optimization of seismic metamaterials to mitigate ground vibration

Ground-borne vibration due to railway traffic is an increasingly important environmental concern. As it may cause malfunctioning of sensitive equipment and discomfort to people. Following earlier developments of metamaterials in the field of electromagnetics, photonics, and phononics, the aim of this research is to design an array of resonators installed between buildings and a railway track for vibration reduction. We develop an optimization method to enhance the performance of the metamaterials constrained by the vibration reduction in a wide frequency range (1-80 Hz) and in an extended volume of soil. The optimization relies on a 3D coupled finite element – boundary element method. The resonators are modeled as a single degree of freedom on top of square concrete foundations while the soil is considered to be a horizontally layered elastic halfspace. In order to develop an optimization method for metamaterials, the dynamic properties of the resonators and their geometrical configuration (distance between the resonators) are considered as design variables. Varying the dynamic parameters of the resonators, uniform and nonuniform configurations are studied. At present, a simplified formulation of the problem is considered, where the vibration reduction at a single point is targeted for a harmonic source, as this is expected to lead to a design that can be interpreted more easily. Local and global optimization methods using a gradient-based algorithm are explored. As expected, the performance in vibration reduction increases with the mass of the resonators. It is also observed how vibration reduction for a harmonic source requires the natural frequency of the resonators to be slightly higher than the frequency of the source. This is due to the fact that dynamic soil-structure interaction results in a lower natural frequency of the oscillator interacting with the soil. Next, the formulation of the optimization problem can be adapted to target vibration reduction over a larger area and in a wider frequency range.