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• A TMDI-controlled primary structure is evaluated under base excitations. • Closed-form tuning formulas of non-grounded TMDI are derived. • Performance of proposed formulas are compared with those in the literature. • Control and dissipation performances are verified under actual ground motions. This research contributes new analytical formulae for H ∞ optimal tuning of non-grounded tuned mass-damper-inerter (TMDI) for minimizing free-end displacement of base-excited cantilevered structures. The derivation relies on the fixed-point theory, making use of single-mode modelling of the cantilevered structure while accommodating arbitrary TMDI placement along the structural height. Optimal TMDI tuning parameters are derived for given dominant mode shape of structure and TMDI inertial properties (i.e., secondary mass and inertance) under two different types of harmonic excitations with frequency-independent displacement and acceleration amplitudes. The applicability of the derived TMDI tuning formulae for response mitigation of lightly damped cantilevered structures under stationary broadband support excitation is established through comparisons with numerically optimal TMDI properties for a wide range of TMDI inertial properties. Moreover, the analytical TMDI tuning formulae derived in this study achieve enhanced structural performance for base-excited structures compared to those from the literature, derived under various modelling assumptions and optimality criteria. Lastly, the potential of the proposed TMDI tuning for structural response mitigation is numerically evaluated by examining displacement, acceleration, and energy dissipation response history data of an experimentally identified reinforced concrete bridge pier model subjected to 100 earthquake ground motion (GM) records. Overall, reported results demonstrate that the derived analytical formulae can significantly extend the practical application of TMDI as a bona fide dynamic vibration absorber for base-excited structures by circumventing the need for computationally demanding numerical TMDI tuning optimization. [Display omitted] [ABSTRACT FROM AUTHOR]

Tuned mass damper inerter (TMDI) has become a popular choice for vibration control in flexible structures, including long-span bridges, due to its superior performance compared to traditional tuned mass dampers (TMDs), such as improved control effect and smaller static displacement. However, the control effect of TMDI is heavily reliant on the spanning distance of inerter, which typically generates a significant internal additional moment due to the force imbalance, limiting the practical application of TMDI on flexible structures. For this reason, a novel lever-arm TMDI (LTMDI) is proposed in this study, to suppress the vibrations of long-span bridges. The non-dimensional governing equations of the bridge-LTMDI system are established in modal coordinates, and the closed-form solutions of the optimum frequency and damping ratios of LTMDI are derived based on the classical fixed-point theory. Parametric studies are conducted to investigate the influences of the fulcrum position, modal shape ratio, mass ratio, inertance ratio and asymmetric mode on the control effectiveness. Moreover, for comparison, the control effectiveness of LTMDI is further compared to those of the TMD and TMDI. Finally, a long-span bridge is selected as an example to demonstrate the effectiveness of LTMDI in reducing vortex-induced vibration (VIV). The results show that the LTMDI has superior control effect and space feasibility as compared to the TMD and TMDI in both frequency and time domains. The derived analytical formulas can accurately determine the optimal parameters, providing a simple yet efficient guideline for the application of LTMDI in flexible structures. [ABSTRACT FROM AUTHOR]