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Optimal design and assessment of tuned mass damper inerter with nonlinear viscous damper in seismically excited multi-storey buildings

Rajana, K., Wang, Z. & Giaralis, A. ORCID: 0000-0002-2952-1171 (2023). Optimal design and assessment of tuned mass damper inerter with nonlinear viscous damper in seismically excited multi-storey buildings. Bulletin of Earthquake Engineering, doi: 10.1007/s10518-022-01609-3


In recent years, the tuned mass damper inerter (TMDI) has been demonstrated in several theoretical studies to be an effective vibration absorber for the seismic protection of non-isolated buildings. Its effectiveness relies on careful tuning of the TMDI stiffness and damping properties, while its performance improves with the increase of the inertance property which is readily scalable. Nevertheless, in all previous studies, the energy dissipative TMDI element has been modelled by a linear viscous damper. Still, commercial viscous dampers display a nonlinear velocity-dependent power law behavior. In this regard, this paper investigates, for the first time in literature, the potential of the TMDI fitted with nonlinear viscous damper (NVD) for seismic response protection of multi-storey buildings. This is supported by an efficient optimal nonlinear TMDI (NTMDI) tuning approach which accounts for any absorber connectivity to the building structure and employs statistical linearization to treat the nonlinear damping term. For the special case of white-noise excited undamped buildings, optimal NTMDI tuning is derived analytically in closed-form which is shown to be sufficiently accurate for lightly damped structures. Comprehensive numerical data are presented to delineate trends of optimal NVD damping coefficient with the NVD power-law exponent and the inertance. Further, nonlinear response history analysis results pertaining to optimally tuned NTMDI application for a benchmark 9-storey steel structure demonstrate that reduced NTMDI stroke and inerter force can be achieved with negligible change in storey drifts and floor acceleration performance by adopting lower NVD exponent values, leading to practically beneficial NTMDI applications.

Publication Type: Article
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Publisher Keywords: Tuned mass damper inerter, nonlinear viscous damper, low-order modelling, optimal tuning, statistical linearization
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
T Technology > TH Building construction
Departments: School of Science & Technology > Engineering
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