A shape memory alloy damping inerter (SDI) with an SMA placed in parallel with an inerter and then in serial with a spring was developed as a vibration control device, where the inerter is utilized to amplify the deformation of SMA to improve the energy dissipation capacity. However, SDI can have other mechanical layouts when an SMA, an inerter and a spring are involved, which may exhibit different control effectiveness. Moreover, explicit design methods aiming to achieve the optimal performance of the SDI systems remain unexplored. In this study, SDIs with different mechanical layouts are proposed and compared, and design method for the SDI-equipped structure is developed. Firstly, the mechanical model of a structure with SDI systems is separately established. Parametric analysis is then conducted in terms of the displacement response, acceleration response and damping enhancement effect. Selection for appropriate SDI mechanical layout can be identified based on parametric analysis results. Additionally, design method based on maximizing the damping enhancement effect to fully develop the energy dissipation capacity of the SMA under the target structural response mitigation ratio is proposed. The performance of the optimal designed SDI-equipped structures is finally evaluated in the time-domain. Results show that both the displacement and acceleration responses of the SDI-equipped structures can be effectively mitigated by using the proposed optimal design method. Among the optimized SDI systems, the energy dissipation capacity of SMA is almost similar. Different SDI systems differ in the energy dissipation characteristic. The SMA-spring-paralleled SDI exhibits minimum damping force, indicating a better damping enhancement effect and less material demand of SMA than the other SDI systems.

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 closedform 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.base isolation, closed-form design formulae, damping enhancement effect, dual-targetoriented design strategy, inerter system | INTRODUCTIONBase isolation technology has been extensively used in earthquake-prone regions to protect the structures from earthquake-induced damage. 1,2 The principle of this technology is to transfer most of the seismic energy to the isolation system, such that the primary structure is almost decoupled from the ground motion and behaves similar to a rigid body. However, in doing this, a relatively large displacement concentrates at the isolation layer, which may occupy a huge space for installation and cause inconvenience to the connection of utilities (gas and water supply system). 3 As a