Improved response spectrum method based on real-complex hybrid modal superposition for base-isolated structures

A novel real-complex hybrid modal response spectrum method (RCHM-RSM) based on the modal superposition of the superstructure is proposed for base-isolated (BI) structures in this paper. In contrast to the traditional analysis method, the method can increase the accuracy of the structural response and avoid complex calculations. Additionally, the direct use of the damping matrix of superstructures for BI structures was found to cause an overestimation of the damping effect and consequently underestimate the deformation of the superstructure. Thus, a new scheme is proposed for determining the damping matrix for BI structures, and general expressions of the damping matrix of the superstructure and the damping constant of the isolation layer are presented. Using the proposed method to construct the damping matrix of BI structures, the equivalent load associated with the coupling damping between the structure and support can be determined when the displacement-velocity input model (D-VIM) is adopted. Analytical expressions of structural matrices are presented for a shear-type model of a BI structure, and a numerical investigation is conducted to demonstrate the feasibility and effectiveness of the proposed methods. The results show that the proposed method (RCHM-RSM) has the advantages of simple calculations and high accuracy. The numerical results obtained also confirm that the direct use of the damping matrix of superstructures for the BI structure will underestimate the superstructure response, while the displacement input model (DIM) overestimates the deformation of the isolation layer and underestimates superstructure responses, the analysis results by using D-VIM are consistent with the acceleration input model (AIM), so the D-VIM should be used instead of the DIM.