Response and Finite Element Analysis of Base-Isolated System with Inerter Under Nonstationary Excitation

In the base isolation system (BIS), most of the seismic-induced displacements are concentrated in the isolation layer, which endures significant displacements. To improve the seismic performance of the isolation layer, this paper proposes an enhanced BIS that incorporates an inerter element. Existing design methods for structures with inerter system often overlook the nonstationary characteristics of earthquakes, resulting in inaccurate prediction of the seismic structure’s response to actual seismicity. Therefore, this paper introduces a quadratic decomposition method of the power spectral density function (QD-PSDF) to obtain the response of BIS under nonstationary random excitation. First, the complex modal method (CMM) and pseudo excitation method (PEM) are used to derive a unified solution for the structural response. Next, the QD-PSDF is employed to derive analytical solutions for spectral moments and nongeometric spectral characteristics (NGSC), which are then used to calculate the inerter system parameters that meet the target performance through reliability formulas. Finally, finite element method (FEM) modeling is used to verify the accuracy and general applicability of this method for structure equipped with inerter system and to discuss the damping effect of two different inerter systems. The research results indicate that the proposed method accounts for the nonstationary state characteristics of seismic excitation, enabling the accurate and efficient calculation of the structure’s nonstationary response spectral moment. This improvement contributes to the reliability of seismic design and enhances the safety of the structure.