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Analytical Design of Non-grounded Tuned Mass-Damper-Inerter for Base-excited Structures

Li, Z., Xu, K., Wang, Z. , Bi, K., Qin, H. & Giaralis, A. ORCID: 0000-0002-2952-1171 (2024). Analytical Design of Non-grounded Tuned Mass-Damper-Inerter for Base-excited Structures. International Journal of Mechanical Sciences, 276, article number 109394. doi: 10.1016/j.ijmecsci.2024.109394


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.

Publication Type: Article
Additional Information: © 2024. This manuscript version is made available under the CC-BY-NC-ND 4.0 license in new tab/window)
Publisher Keywords: Base-excited cantilevered structures, vibration control, tuned mass damper inerter, non-grounded configuration, analytical optimization design
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
T Technology > TH Building construction
Departments: School of Science & Technology
School of Science & Technology > Engineering
SWORD Depositor:
[thumbnail of Li et al_IJMS_2024_authors version.pdf] Text - Accepted Version
This document is not freely accessible until 16 May 2025 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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