Modeling, Design, and Laboratory Testing of a Passive Friction Seismic Metamaterial Base Isolator (PFSMBI)

This paper focuses on the theoretical and analytical modeling of a novel seismic isolator termed the Passive Friction Mechanical Metamaterial Seismic Isolator (PFSMBI) system, which is designed for seismic hazard mitigation in multi-story buildings. The PFSMBI system consists of a lattice structure composed of a series of identical small cells interconnected by layers made of viscoelastic materials. The main function of the lattice is to shift the fundamental natural frequency of the building away from the dominant frequency of earthquake excitations by creating low-frequency bandgaps (FBGs) below 20 Hz. In this configuration, each unit cell contains an inner resonator that slides over a friction surface while it is tuned to vibrate at the fundamental natural frequency of the building. This resonance enhances the energy dissipation capacity of the PFSMBI system. After deriving the governing equations for four selected lattice configurations (i.e., Cases 1-4), a parametric study is performed to optimize the PFSMBI system for a wide range of harmonic ground motion frequencies. In this study, we examine how key parameters, such as the mass ratios of the cells and resonators, tuning frequency ratios, the number of cells, and the coefficient of friction, affect the system's performance. The PFSMBI system is then incorporated into the dynamic model of a six-story base-isolated building to evaluate its effectiveness in reducing the floor acceleration and inter-story drift under actual earthquake ground motion records. This dynamic model is used to investigate the effect of stick-slip motion (SSM) on the energy dissipation performance of a PFSMBI system by employing the LuGre friction model. The numerical results show that the optimized PFSMBI system, through its lattice structure and frictional resonators, effectively reduces floor acceleration and inter-story drift by leveraging FBGs and frictional energy dissipation, particularly when SSM effects are properly accounted for. Finally, a small-scale prototype of the PFSMBI system with two cells is developed to verify the effect of SSM. This experimental validation highlights that neglecting SSM can lead to an overestimation of the energy dissipation performance of PFSMBI systems.