Real-complex hybrid modal response spectrum method for seismically base-isolated structures

In this study, a novel real-complex hybrid modal response spectrum method (RCHM-RSM) for seismically base-isolated (BI) structures is proposed, which only applies the modal analysis to a superstructure, avoiding the complex calculation. In contrast to the complex modal response spectrum method (CM-RSM), the RCHM-RSM is more reliable and easier to understand. Additionally, analytical expressions of the structural modal matrices are developed for seismically BI structures. A regular model and an irregular model of BI structures are developed to investigate the impact of the proposed method on the solution accuracy. The results show that the proposed method demonstrated its advantages of simple calculations and a high accuracy for two models. The maximum relative deviation of the superstructure story displacement and inter-story are 12.32% and 12.52% for the irregular BI structure, respectively, by comparing them with the response history analysis (RHA). Additionally, the forced decoupling response spectrum method (FD-RSM) significantly underestimates the superstructure response, the maximum relative deviation of the superstructure story displacement and inter-story displacement are 26.56% and 31.56%. The numerical results obtained also confirm that using the Bernoulli-Euler model to idealize the superstructure significantly underestimates the response of the superstructure, and the roof displacement is underestimated by 53%.