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Inerter-based vibration absorbers (IVAs), such as the tuned-mass-damper-inerter (TMDI), have become popular in recent years for the earthquake protection of building structures. Previous studies using linear structural models have shown that IVAs can achieve enhanced vibration suppression, but at the expense of increased control forces exerted from the IVA to the host building structure. The authors recently developed a bi-objective IVA design framework for linearly behaving buildings to balance between structural performance (drift/acceleration suppression) and IVA forces. This paper extends the framework to multi-storey hysteretic/yielding structures under seismic excitation. Though the proposed design framework can accommodate any type of IVA, the focus is herein on TMDI applications, with tuned-mass-damper (TMD) and tuned-inerter-damper (TID) treated as special cases of the TMDI. Earthquake hazard is modeled through representative, design-level acceleration time-histories and response of the IVA-equipped structure is evaluated through nonlinear response-history analysis. A high-fidelity finite element model (FEM) is established to accurately describe hysteretic structural behavior. To reduce the computational burden, a reduced order model (ROM) is based on the original FEM, using the framework proposed recently by the first and second authors. The ROM maintains the accuracy of the original FEM while enabling for a computationally efficient solution to the optimization problem. As an illustrative example, the bi-objective design for different IVA placements along the height of a non-linear benchmark 9-storey steel frame structure is examined. The accuracy of the ROM-based design is evaluated by comparing performance to the FEM-based response predictions across the entire Pareto front resulting from the bi-objective optimization. Then, the designs and associated performance predicted by using a linear or a nonlinear structural model are compared to evaluate how the explicit consideration of nonlinearities, as well as the degree of nonlinear behavior, impact the IVA design and efficiency.

Tuned-mass-damper-inerter optimal design and performance assessment for multi-storey hysteretic buildings under seismic excitation