Dynamic characterization of multiple tuned mass dampers and some design formulas
Abstract
Multiple Tuned Mass Dampers (MTMD) consist of a large number of small oscillators with natural frequencies distributed around the natural frequency of a controlled mode of the structure. In the present paper, the modal characteristics and efficiency of the MTMD are studied analytically. Perturbation solutions for the modal properties of the MTMD–structure system are obtained and the modal characteristics are discussed. An explicit formula to estimate the effectiveness of the MTMD subjected to harmonic forces is also derived. It is shown that the MTMD is efficient when at least one of the oscillators is strongly coupled with the structure in any mode. Based on this observation, a critical bandwidth of the natural frequencies of the MTMD to make the system multiply tuned is derived in a simple form, and furthermore a robustness criterion for the frequency tuning under a given bandwidth is proposed. It is shown that, when properly designed, the MTMD can be much more stable (robust) than a conventional single TMD while maintaining more or less the same efficiency. Numerical studies verify the accuracy of the perturbation solutions and the proposed formulas.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Multiple tuned mass dampers (MTMD) can be more effective than a single TMD with equal mass and damping ratio.
“It has been observed that MTMD can be more effective than a single TMD with equal mass and damping ratio and the optimum parameters of the MTMD system are obtained for different mass ratio and number of dampers.”
From Application of Tuned Mass Dampers for Structural Vibration Control: A State-of-the-art Review (2020) · cites this paper as [126]
Optimum parameters of an MTMD system are obtained for different mass ratios and numbers of dampers.
“It has been observed that MTMD can be more effective than a single TMD with equal mass and damping ratio and the optimum parameters of the MTMD system are obtained for different mass ratio and number of dampers.”
From Application of Tuned Mass Dampers for Structural Vibration Control: A State-of-the-art Review (2020) · cites this paper as [126]
Cited by
Sorted by citations
Research developments in vibration control of structures using passive tuned mass dampers
Elias, S., & Matsagar, V. (2017) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2017.09.015 · Cited by 545 · see citing works
Performance of Multiple Mass Dampers under Random Loading
Kareem, A., & Kline, S. (1995) · Journal of Structural Engineering · doi:10.1061/(asce)0733-9445(1995)121:2(348) · Cited by 306 · see citing works
Nagarajaiah, S. (2009) · Structural Control and Health Monitoring · doi:10.1002/stc.349 · Cited by 256 · see citing works
Application of Tuned Mass Dampers for Structural Vibration Control: A State-of-the-art Review
Rahimi, F., Aghayari, R., & Samali, B. (2020) · Civil Engineering Journal · doi:10.28991/cej-2020-03091571 · Cited by 138 · see citing works
“Abé and Fujino [41] utilizing the perturbation solutions, formulas relevant to designing the TMD for different types of loading are gotten; they are claimed as a function of mass ratio, tuning ratio, damping ratio of the TMD and damping ratio of the structure.”
MethodInfluentialDistributed Mass Damper System for Integrating Structural and Environmental Controls in Buildings
Fu, T. S., & Johnson, E. A. (2011) · Journal of Engineering Mechanics · doi:10.1061/(asce)em.1943-7889.0000211 · Cited by 53 · see citing works
- Authors
- Abé, M., & Fujino, Y.
- Affiliations
- Northwestern University (US)
- The University of Tokyo (JP)
- ORCID
- Fujino, Yozo
- Venue
- Earthquake Engineering & Structural Dynamics
- Publisher
- Wiley
- Published
- 1994-08
- Volume
- 23
- Issue
- 8
- Pages
- 813-835
- ISSN
- 0098-8847 (ISSN-L)
- 1096-9845
- OpenAlex
- W1996629181
- Cited by
- 329
- References
- 0
- Citations by year
- 2026: 14 · 2025: 17 · 2024: 14 · 2023: 15 · 2022: 24 · 2021: 18 · 2020: 15 · 2019: 19 · 2018: 14 · 2017: 11 · 2016: 9 · 2015: 10 · 2014: 12 · 2013: 8 · 2012: 7
- FWCI
- 13.94
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Earthquake Engineering & Structural Dynamics (publishedVersion)
- Topics
- Physical Sciences › Engineering › Civil and Structural Engineering › Vibration Control and Rheological Fluids
- Physical Sciences › Engineering › Civil and Structural Engineering › Structural Engineering and Vibration Analysis
- Physical Sciences › Engineering › Control and Systems Engineering › Vibration and Dynamic Analysis
- Keywords
- multiple tuned mass dampers, tuned mass damper, structural vibration control, modal parameters, perturbation solution, harmonic excitation, damper effectiveness, critical bandwidth, single-degree-of-freedom systems
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
