Seismic Resonant Metamaterials for the protection of an elastic-plastic SDOF system against vertically propagating seismic shear waves (SH) in nonlinear soil

Abstract

The paper explores the key mechanisms that govern the dynamic interaction between resonant metamaterials (consisting of multiple unit cells embedded in the soil, with horizontally vibrating internal masses) and an existing nonlinear structure on nonlinear soil. Elastic behavior of the soil and of the SDOF system, representing the structure, is also investigated for deeper insights. Employing the Real-ESSI Simulator, 2D finite element (FE) models are developed and used to conduct an extensive parametric analysis, evaluating the influence of key parameters on the protective efficiency of resonant metamaterials. Both artificial and real motions are used as seismic excitation, vertically propagated through the soil as shear waves (SH), employing the Domain Reduction Method (DRM). Two protective mechanisms are identified. The first one is related to the inertial interaction of the metamaterials with the surrounding soil: out-of-phase resonant oscillation of internal masses with respect to the soil at periods close to the natural period of the structure. The maximum reduction in structural response is achieved when the resonant period of the metamaterials is equal or a bit larger than the effective period of the structure. The second mechanism is related to the kinematic interaction of the metamaterials with the surrounding soil: the presence of empty unit cells (no vibrating masses) in the soil next to the structure creates a protective “shadow” zone. This kinematic interaction mechanism becomes effective when the wavelength of the incoming seismic waves is comparable to the embedment depth of the metamaterials, and at the same time, the period of the waves is close to the natural period of the structure. When both soil and structural nonlinearities are considered, the effect of metamaterials is always beneficial, and their action is localized, making them practically harmless for neighboring structures.