Effects of Different Frequency Sensitivity Models of a Viscoelastic Damper on Wind-Induced Response of High-Rise Buildings
Abstract
:1. Introduction
2. Target Building and Numerical Models
2.1. Target Building and the SDOF Model
2.2. Basic Settings of Numerical Models with the VE Damper
2.3. FD Model and ID Models
2.3.1. FD Model
2.3.2. 4-Element Model
2.3.3. 6-Element Model
3. Characteristics of the VE Systems under the Steady-State Response
- -
- When subjected to harmonic waves of , the hysteresis loop (Figure 8a) of the 4-element model is smaller than the FD model. While the hysteresis loop of the 6-element model is greater than the FD model. The massive difference in the hysteresis loop of the damper among three models when aligns with the relationship of frequency sensitivity in Figure 6.
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- -
4. Characteristics of the VE Systems under the Wind-Induced Response
4.1. Wind Force
4.2. Wind-Induced Response of FD Systems
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- In Figure 12a, the along-wind displacement has high power with wide-band frequencies in the low-frequency region. However, the across-wind displacement has high power around 1.0 Hz.
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- In Figure 12b, the along-wind velocity has high power close to the resonance frequency (). In contrast, the across-wind velocity spectrum has high power in a range from 1.0 Hz to the resonance frequency ().
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- In Figure 12c, the along-wind acceleration has a similar tendency with its velocity, having high power close to the resonance frequency (). Similarly, the across-wind acceleration has high power close to the resonance frequency.
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- In Figure 13a, the along-wind displacement has significantly high power close to the resonance frequency () and a wide band of the low-frequency region. However, the across-wind displacement has high power between 1.0 Hz and the resonance frequency ().
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4.3. Response Comparison between ID Systems and FD System in Along-Wind
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- The mean, maximum, and standard deviation of the along-wind displacement of the 4-element system is smaller than the FD system. It shows that the difference increases as the storage stiffness of the damper increases.
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- When the ratio of storage stiffness of the damper is 2.0 (as an added component is -HH or -HS), the difference of the mean, maximum, and standard deviation of the along-wind displacement between the 4-element system and the FD system is about .
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- The differences in the maximum and standard deviation of the along-wind velocity and acceleration of the 4-element system remain aligned with the FD system.
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- The mean, maximum, and standard deviation of the along-wind displacement of the 6-element system is larger than the FD system. It shows that the difference increases as the storage stiffness of the damper increases.
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- When the ratio of storage stiffness of the damper is 2.0 (as an added component is -HH or -HS), the difference of the mean, maximum, and standard deviation of the along-wind displacement between the 6-element system and the FD system is over . In contrast, when the ratio of storage stiffness of the damper is 0.4 (as an added component is -SH or -SS), the difference of the mean, maximum, and standard deviation of the along-wind displacement between the 6-element system and the FD system is about .
- -
- The differences in the maximum and standard deviation of both along-wind velocity and acceleration of the 6-element system also remain aligned with the FD system.
4.4. Response Comparison between ID Systems and FD System in Across-Wind
5. Conclusions
- -
- The along-wind displacement of the 4-element and 6-element systems with the dampers of high storage stiffness has obvious differences with the FD system due to low frequency and the wide-band frequencies dominating the behavior of the VE system significantly. Furthermore, the frequency sensitivity of the 4-element and 6-element systems and the FD system have massive differences at low frequencies.
- -
- The along-wind displacement of the 4-element and 6-element systems with the dampers of low storage stiffness has better agreement with the FD system due to the resonance frequency dominating the behavior of the VE systems significantly, and the frequency sensitivity of VE systems having good agreements at the resonance frequency. Similarly, the hysteresis loops of the 4-element and 6-element systems with low storage stiffness align well with the FD system. The energy dissipation and the mean deformation of the 4-element and 6-element systems are also matching well with the FD system, respectively.
- -
- The responses and the hysteresis loops of the 4-element and 6-element systems have good agreements with the FD system due to the narrow-band frequencies being close to the resonance frequency along with the alignment of frequency sensitivity at resonance frequency dominating the across-wind response, which is more tremendous than the along-wind response.
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- The energy dissipation of the 6-element systems has better matching with the FD systems than the 4-element systems since the 6-element system has better agreement with the FD system at the resonance frequency than the 4-element system.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. Frequency Sensitivity of the Damping Coefficient in the VE System
Appendix B. Numerical Integration Method of the Fractional Derivative Model [18,27]
Appendix C. Effect of Window Time
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System | Damper | Brace | |||
---|---|---|---|---|---|
1H-HH | 2 s | Hard | Hard | ∞ | |
1H-SH | 2 s | Soft | Hard | ∞ | |
1H-HS | 2 s | Hard | Soft | ||
1H-SS | 2 s | Soft | Soft | ||
2H-HH | 4 s | Hard | Hard | ∞ | |
2H-SH | 4 s | Soft | Hard | ∞ | |
2H-HS | 4 s | Hard | Soft | ||
2H-SS | 4 s | Soft | Soft | ||
3H-HH | 6 s | Hard | Hard | ∞ | |
3H-SH | 6 s | Soft | Hard | ∞ | |
3H-HS | 6 s | Hard | Soft | ||
3H-SS | 6 s | Soft | Soft |
FD Model | 4-Element Model | 6-Element Model | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Frame | System | |||||||||||||
[Hz] | [m] | [] | [] | [] | [] | [] | [] | [] | [] | [] | [] | |||
1H-HH | ||||||||||||||
1H | 1H-SH | |||||||||||||
(0.01 H) | 1H-HS | |||||||||||||
1H-SS | ||||||||||||||
2H-HH | ||||||||||||||
2H | 2H-SH | |||||||||||||
(0.02 H) | 2H-HS | |||||||||||||
2H-SS | ||||||||||||||
3H-HH | ||||||||||||||
3H | 3H-SH | |||||||||||||
(0.03 H) | 3H-HS | |||||||||||||
3H-SS |
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Sato, D.; Chang, T.-W.; Chen, Y. Effects of Different Frequency Sensitivity Models of a Viscoelastic Damper on Wind-Induced Response of High-Rise Buildings. Buildings 2022, 12, 2182. https://doi.org/10.3390/buildings12122182
Sato D, Chang T-W, Chen Y. Effects of Different Frequency Sensitivity Models of a Viscoelastic Damper on Wind-Induced Response of High-Rise Buildings. Buildings. 2022; 12(12):2182. https://doi.org/10.3390/buildings12122182
Chicago/Turabian StyleSato, Daiki, Ting-Wei Chang, and Yinli Chen. 2022. "Effects of Different Frequency Sensitivity Models of a Viscoelastic Damper on Wind-Induced Response of High-Rise Buildings" Buildings 12, no. 12: 2182. https://doi.org/10.3390/buildings12122182