<b>Optimal and seismic response analysis of Inter-story Isolation System </b><b>with tuned inerter damper</b><b>(IIS-TID)</b>

The optimal and seismic performance of the inter-story isolation with tuned inerter damper(IIS-TID) is studied using simplified 3-degree-of-freedom (3DOF) and multi-degree-of-freedom (MDOF) models. Firstly, a 3DOF motion governing equation is used to derive the seismic response variance of the substructure, superstructure and isolation layer of IIS-TID system under white noise excitation. The effects of Structural and TID parameters on enhanced control are analyzed.Considering different objective functions, the frequency and damping parameters are optimized and the simplified expression of the optimal TID with each structure parameter are conducted. Further, comparison of the seismic response of the IIS with and without TID is made by using a MDOF model example.under ordinary and near fault earthquake excitation. Finally,the sensitivity of the optimized design parameters of the TID are analyzed as reference for engineering practice. The results illustrate the TID system is effective to control acceleration and story drift responses of the substructure, superstructure and isolation layer of the IIS, especially for isolation displacement and substructure acceleration .本研究采用简化三自由度（3-degree-of-freedom，3DOF）模型与多自由度（multi-degree-of-freedom，MDOF）模型，对带调谐惯容阻尼器（tuned inerter damper，TID）的层间隔震系统（IIS-TID）的最优设计性能与抗震性能展开研究。首先，基于三自由度运动控制方程，推导白噪声激励下IIS-TID系统下部结构、上部结构及隔震层的地震响应方差，分析结构参数与TID参数对减震控制效果的影响。针对不同优化目标，对TID的频率与阻尼参数开展优化，并推导得到适配各结构参数的最优TID简化表达式。进一步，通过多自由度模型算例，对比普通地震与近断层地震激励下，加装TID与未加装TID的层间隔震系统的地震响应差异。最后，分析TID优化设计参数的灵敏度特性，为工程实践提供参考依据。研究结果表明，TID系统可有效管控IIS-TID系统下部结构、上部结构与隔震层的加速度及层间位移响应，尤其对隔震位移与下部结构加速度的控制效果更为显著。