On the displacement control performance of base-isolated structures incorporating nonlinear negative stiffness device

Low -frequency dominant far -field harmonic -like long period ground motions (FGMs) excitations have the potential to amplify the seismic response of base -isolated structures (BIS) and may result in isolator displacements exceeding their maximum limits. The application of negative stiffness devices (NSD) in isolated structures primarily focuses on SDOF systems, which fails to capture the displacement response of the superstructure on the isolation story. To address this issue, this study proposes the application of NSD to a 2DOF system in a BIS, with root mean square value as the metric for displacement transmissibility. Firstly, the displacement transmissibility of base -isolated structures with negative stiffness devices (BIS-NSD) and BIS is derived using the triple -harmonic balance (T-HB) method and the single -harmonic balance (S-HB) method, respectively. Subsequently, the applicability of the T-HB method and the S-HB method in obtaining analytical solution for the displacement transmissibility of BIS-NSD and BIS is revealed and validated through numerical solution. Parameters are selected based on fixed-point theorem for comparative analysis of the displacement and acceleration transmissibility between BIS-NSD and BIS. Finally, a comparative analysis between BIS-NSD and BIS under FGMs confirms the application advantages of NSD. The results indicate that compared to BIS, BIS-NSD significantly reduces the displacement transmissibility of the superstructure and the isolation story in the low -frequency range. As the primary resonance frequency decreases, NSD widens the vibration bandwidth of BIS. BIS-NSD effectively mitigates the increase in displacement caused by low -frequency ground motions. The acceleration transmissibility demonstrates that, without sacrificing the acceleration of the superstructure, it effectively controls the displacement of the isolation story.