Closed‐form design formulae for seismically isolated structure with a damping enhanced inerter system

Abstract

Existing studies mainly focused on the mass enhancement effect of the inerter system within a seismically isolated structure. In this study, a new analytical perspective is introduced based on another attractive feature of the inerter system, namely, the damping enhancement effect. Accordingly, a ready-to-use optimal design method for isolated structure with the inerter system is proposed. First, the damping enhancement equation of the inerter system is reformulated in the form of the equivalent damping ratio. Then, the closed-form design formulae of the inerter system are derived based on damping enhancement maximization and seismic demand. By taking the performance of both the primary structure and the isolation layer into consideration, the dual-target-oriented design strategy of the isolated structure is subsequently developed. And the closed-form design formulae of the inerter system are then integrated into the strategy to produce a practical design method for isolated structure with the inerter system. A seven-story isolated benchmark model is finally employed as the design case to exemplify the effectiveness of the proposed design method. Compared to the directly installed viscous damper, structural base shear force, inter-story drift angle, and the deformation of the isolation layer are more effectively reduced with the addition of the inerter system, and the energy dissipation capacity of the damper within the inerter system is improved substantially. Furthermore, the derived closed-form design formulae reduce the burden of iterative calculation and bring a high-efficient design for isolated structure with the inerter system.