The Influence of Viscoelastic Model on Seismic Response Mitigation Performance of Optimized Inerter-Based Tuned Mass Damper

The inerter element can be integrated with the tuned mass damper (TMD) to form a more lightweight and high-performance tuned mass damper inerter (TMDI), which has been widely applied to mitigate seismic responses in various engineering structures. However, the influence and applicability of viscoelastic models on the performance of TMDI have not yet been fully revealed. To address this issue, this study derives the optimal nominal damping ratio and stiffness ratio of an inerter-based TMD with a Maxwell viscoelastic model (Maxwell mass damper inerter, MMDI) using [Formula: see text] optimization and conducts a comparative analysis with the classical TMDI, which incorporates a Kelvin viscoelastic model. The influence of different viscoelastic models on the optimized parameters and vibration mitigation performance of inerter-based TMDs is also examined. Results show that MMDI consistently exhibits larger optimal parameters than TMDI, particularly in damping ratio. Under stochastic excitation, MMDI provides superior displacement control, especially in reducing root mean square displacement, whereas TMDI achieves better acceleration control. In terms of energy dissipation, MMDI is more effective under high-frequency seismic inputs, while TMDI performs better for low-frequency excitations. However, under broadband excitation, MMDI demonstrates slightly superior overall energy dissipation. Moreover, the damping mechanism of MMDI, characterized by low displacement and high damping force, ensures greater long-term operational stability compared to TMDI, which relies on large deformations for energy dissipation. This advantage, however, comes at the cost of higher manufacturing and implementation expenses. In the mitigation of seismic responses for multi-degree-of-freedom (MDOF) structures, compared to TMDI in displacement control, MMDI is less affected by the connection of non-grounded inerter. Its displacement control performance is closer to that of the ideal grounded inerter case and is more effective for broadband seismic input. However, TMDI remains more suitable for acceleration control in MDOF structures. The introduction of MMDI could offer an alternative solution for mitigating seismic responses in complex engineering structures where conventional TMDI systems may be insufficient. This work could also provide reference for the optimization and performance evaluation of topological combinations of inerter-based dampers.