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Dynamic characteristics of non‐classically damped structures
Abstract
The equations of motion of a structure in undamped modal coordinates may have non‐zero off‐diagonal terms in the damping matrix. Although these terms are commonly neglected, studies have shown that they may have a significant influence on the response to dynamic loads. In this paper, two independent criteria are developed to determine when these damping terms will affect the structure's modal properties and response. It is found that even small off‐diagonal damping values can be significant if the structure has closely spaced natural frequencies. To quantify and understand the influence of these damping terms, closed‐form analytical expressions are derived for the modal properties and harmonic and stochastic response of structures with closely spaced natural frequencies. One conclusion is that off‐diagonal damping terms will decrease a modal damping ratio for each pair of closely spaced modes. This is significant, since a response analysis performed by neglecting these off‐diagonal terms will underestimate the true response.
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Multiple TMDs can be made more effective than a conventional optimal single TMD of the same total mass, and the performance of multiple TMDs is less sensitive to uncertainties in the parameters of the system.
“It has shown that multiple TMDs can be made more effective than a conventional optimal single TMD of the same total mass and, furthermore, performance of multiple TMDs is less sensitive to uncertainties in the parameters of the system.”
From Application of Tuned Mass Dampers for Structural Vibration Control: A State-of-the-art Review (2020) · cites this paper as [39]
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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 556
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
“The MTMD systems with a uniform propagation of natural frequencies were first proposed by Xu and Igusa [19] and then further investigated by Li and Liu [81]; Pansare and Jangid [147].”
BackgroundInfluential
Metadata
- Authors
- Xu, K., & Igusa, T.
- Affiliations
- Northwestern University (US)
- ORCID
- Igusa, Takeru
- Venue
- Earthquake Engineering & Structural Dynamics
- Publisher
- Wiley
- Published
- 1991-01
- Volume
- 20
- Issue
- 12
- Pages
- 1127-1144
- ISSN
- 0098-8847 (ISSN-L)
- 1096-9845
- OpenAlex
- W1974382519
- Cited by
- 21
- References
- 0
- Citations by year
- 2025: 1 · 2023: 1 · 2022: 2 · 2020: 1 · 2017: 2
- FWCI
- 1.77
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Earthquake Engineering & Structural Dynamics (publishedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Engineering › Mechanical Engineering › Vibration and Dynamic Analysis
- Physical Sciences › Engineering › Civil and Structural Engineering › Structural Health Monitoring Techniques
- Physical Sciences › Engineering › Civil and Structural Engineering › Vibration Control and Rheological Fluids
- Keywords
- non-classical damping, damping matrix, closely spaced natural frequencies, modal damping ratio, modal properties, harmonic response, stochastic response, dynamic response of structures, modal coordinates
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