Optimal design and performance assessment of enhanced TMDI with tuned inerter-based dampers

To enhance the control performance of a tuned mass damper (TMD) while reducing the tuned mass demand, this paper introduces a novel vibration mitigation strategy: the tuned mass-damper-inerter (TMDI) enhanced by tuned inerter-based dampers (TMDI-TIBD). This study formulates equations of motion and transfer functions for single-degree-of-freedom (SDOF) structures equipped with TMDI-TIBD. Closed-form optimal design formulas are derived using fixed-point theory to minimize displacement and acceleration amplitudes. The control performance of TMDI-TIBD is evaluated through comparative analyses of structural responses, tuned mass stroke, and detuning effect, compared to the TMD and TMDI strategies. TMDI-TIBD is applied to a base-isolated system (BIS) to enhance the vibration isolation performance, with time-history responses compared under seismic excitation. In general, the proposed TMDI-TIBD maintains higher control performance, stronger control robustness, and lower tuned mass demand compared to conventional TMD. In addition, TMDI-TIBD shows a significant improvement in control performance and robustness for structures subjected to harmonic excitation compared to TMDI, regardless of the slightly amplified tuned mass stroke. In summary, TMDI-TIBD leverages the triple-tuning effect of TIBD-enhanced TMD and the mass amplification effect of the inerter, which is a more flexible and adaptable strategy for vibration control of different types of structures.