Seismic Response Analysis of Over-Track Isolated High-Rise Structures Based on a Discrete-Continuous Hybrid Model

As a distinctive typology within the transit-oriented development (TOD) framework, over-track isolated high-rise structures are characterized by constrained substructure heights, fixed isolation layer positions, and superstructures configured as high-rise shear wall systems. In this study, a discrete-continuous hybrid model is developed, in which the substructure and isolation layer are idealized as a lumped-mass system, while the superstructure is modeled as a Timoshenko continuous beam. To capture the nonlinear behavior of isolators across varying ductility levels, the equivalent linearization (EL) model of isolators was proposed through a grey wolf optimization (GWO)-based method. A modal displacement contribution analysis method, combined with the boundary conditions of the hybrid model, is proposed to identify the minimum number of significant and participating modes. The amplitude of the structural seismic response is then determined using complex mode response spectrum analysis. The effects of mass ratio and isolator stiffness on dynamic behavior and energy dissipation mechanisms are also investigated. Results indicate that the number of participating modes of shear walls is jointly determined based on the dynamic characteristics of shear wall structures and the modal displacement of the overall system for the over-track isolated high-rise structure. Relative to the full-mode analysis, the discrete–continuous hybrid model with the minimum number of modes exhibited maximum deviations of 1.67% in displacement, 4.14% in acceleration, and 2.73% in internal force. Under artificial ground motions, the displacement of the isolation layer obtained by the Bouc–Wen EL method exhibited deviations between −9.75% and −2.47% relative to nonlinear results across different earthquake intensities. For near-field, near-field with pulse, and far-field records, the maximum deviations were −25.16%, −15.40%, and −16.65%, respectively. Energy dissipation mechanisms depend on structural parameters: when the mass ratio [Formula: see text] and relative isolation height [Formula: see text], mass damping dominates; when [Formula: see text] and [Formula: see text], base isolation prevails; in the intermediate range, a hybrid mechanism emerges, combining both effects.