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

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 comparison. The Real-ESSI Simulator is employed to develop in-plane (2D) finite element (FE) models, and an extensive parametric analysis is conducted to evaluate the influence of key parameters on the protective efficiency of resonant metamaterials. Both artificial and real ground 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 mechanism is related to the inertial interaction of the metamaterials with the surrounding soil, namely, it is the out-of-phase resonant oscillation of the internal metamaterial 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, namely, the presence of empty unit cells (no internal 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 size 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 remains always beneficial, and their action is localized, making them practically harmless to neighboring structures.