TMD Design by an Entropy Index for Seismic Control of Tall Shear-Bending Buildings
2.1. Shear-Bending Lumped Mass Model
2.2. HSV-Based Entropy Index
2.2.1. The Entropy Based on Hankel Singular Values (HSVs)
2.2.2. Vibration Reduction Evaluation of TMDs
3. Building Information
4. HSV Indices of the Structure with and without TMD
4.1. Entropy Index Ratios
- Transfer Equation (10) into a modal form, and then calculate grammians and .
- Calculate by Equation (13), and then the index of the uncontrolled building (without TMD) by Equation (18), including inter-story drifts and acceleration .
- Calculate of the controlled building with TMD tuning to the first three modes and placing on stories 4–12 in turn, to get a 3 × 12 matrix, as the flow chart is shown in Figure 4.
- Figure out the TMD location case with maximum index reduction for each tuning.
4.2. Validation by Responses to White Noise Excitation
4.3. Comparison with the Shear Structure Model
5. Earthquake Responses of TMD Controlled Shear-Bending Structure
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
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|frame k0 (108)||14.3||17.2||16.9||16.1||14.9||14.1||13.7||12.6||11.3||9.85||8.15||5.20|
|wall ks (108)||65.3||35.5||23.5||17.3||13.5||10.8||8.65||6.89||5.34||3.90||2.51||1.14|
|wall kb (108)||5260||2250||1420||967||701||500||353||241||155||90.6||43.8||13.7|
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Wang, Y.; Qu, Z. TMD Design by an Entropy Index for Seismic Control of Tall Shear-Bending Buildings. Entropy 2023, 25, 1110. https://doi.org/10.3390/e25081110
Wang Y, Qu Z. TMD Design by an Entropy Index for Seismic Control of Tall Shear-Bending Buildings. Entropy. 2023; 25(8):1110. https://doi.org/10.3390/e25081110Chicago/Turabian Style
Wang, Yumei, and Zhe Qu. 2023. "TMD Design by an Entropy Index for Seismic Control of Tall Shear-Bending Buildings" Entropy 25, no. 8: 1110. https://doi.org/10.3390/e25081110