Design and optimization of seismic metamaterials to mitigate ground vibration

Abstract

Abstract This paper presents a first step towards developing an optimization method to improve the vibration mitigation performance of seismic metasurfaces. Two alternative objective functions are considered in the optimization problem. First, the vibration at a single receiver due to a harmonic source is minimized. Second, the energy dissipated by the metasurface during harmonic excitation is maximized. The dynamic properties of the resonators are the design variables. Forward modelling relies on a 3D coupled finite element-boundary element method, where the resonators are modeled as single-degree-of-freedom systems on top of square concrete foundations that are positioned on a homogeneous halfspace. A local optimization method with a gradient-based algorithm is used. In both cases, significant vibration reduction is obtained at the target frequency. When the vibration amplitude is minimized, resonators with a mass equal to the maximum allowed mass are obtained, whereas resonators with a lower mass are found when the energy dissipation is maximized. Dynamic soil-structure interaction requires the natural frequency of the resonators to be slightly higher than the excitation frequency. The optimization formulation needs to be further adapted to target vibration reduction over a larger area and in a wider frequency range.