Study on the Influence and Optimization Design of Viscous Damper Parameters on the Damping Efficiency of Frame Shear Wall Structure
Abstract
:1. Introduction
2. Methodology
2.1. Optimization Method for Damper Parameters Based on Response Surface Method
2.1.1. Establishment of Response Surface Model
2.1.2. Solution of Extremum for Multivariate Function
- Assume the bi-variate function is . Calculate the first-order partial derivatives and set them equal to zero to find the stationary point p0, as shown in Equation (6).
- Calculate the second-order partial derivatives of p0 and obtain the coefficients A, B, and C, as shown in Equation (7).
- Determine the extremum situation obtained, as shown in Equation (8).
2.2. Engineering Case on the Optimization of Damper Parameters in Frame Shear wall Structure
2.2.1. Engineering Overview
- Determine the target additional damping ratio added to the structure by the viscous dampers. In this study, a value of 3.0% is considered.
- The formula for calculating the additional damping ratio through the energy method is used to deduce the total damping coefficient and the selected damping exponent required for the structure under the target additional damping ratio. The detailed procedure of this derivation can be referred to in reference [41].
- Divide the total damping coefficient by the damping coefficient of a single damper to obtain the number of dampers. The damping coefficient and exponent of a single damper are generally selected based on engineering experience. In this study, the damping coefficient is taken as C = 60 kN/(mm/s)0.25, and the damping exponent α is 0.25.
- Determine the number and placement of dampers in each floor. The dampers are typically arranged in a simplified manner with uniform distribution in height, and the placement is the same so as not to affect the functionality of the building. Therefore, in this study, the number and placement of viscous dampers are the same for the 1st to 5th floors. Four sets of dampers are arranged in the X and Y directions on each floor, resulting in a total of 40 sets of dampers. The arrangement diagram of dampers is shown in Figure 1a.
2.2.2. Finite Element Model Establishment and Earthquake Waves Selection
3. Results and Discussion
3.1. Sensitivity Analysis of the Impact of Damping Parameters
3.1.1. The Additional Damping Ratio
3.1.2. The Reduction Rate of Vertex Displacement
3.1.3. The Reduction Rate of Base Shear
3.1.4. The Inter-Story Displacement Utilization Rate
3.1.5. Damping Force and Displacement
3.2. Optimization of Parameters for Viscous Dampers and Flowchart for Damping Design
3.2.1. Response Surface Model
3.2.2. Objective Function
3.2.3. Analysis of Optimized Results
3.2.4. The Damping Design Flowchart
4. Conclusions
- (1)
- The parameters within the range of damping coefficient 20~120 kN/(mm/s)α and damping exponent 0.15~0.65 are combined, and the traditional sensitivity analysis method is used to calculate various damping efficiency indicators. When the damping coefficient and damping exponent are approximately (60, 0.25), the additional damping ratio, reduction rate of vertex displacement, and reduction rate of base shear achieve relatively large values of 4.05%, 23%, and 19%, respectively. As the damping coefficient and damping exponent increase, the inter-story displacement utilization rate decreases from significantly greater than 1.0 to far less than 1.0, and the displacement of the damper decreases while the damping force increases. The study shows that the influence of different combinations of viscous damper parameters on the response of damping efficiency indicators is complex, and it is difficult for the traditional sensitivity analysis method to comprehensively consider the combined effects of different damping efficiency indicators to obtain the optimal parameters.
- (2)
- By explicitly formulating the relationship between viscous damper parameters and various damping efficiency indicators of the structural system using response surface methodology, and combining the F-test and coefficient of determination R2 to evaluate the fitting effect of the response surface function, high fitting accuracy and good predictability are achieved, making our model suitable as an optimization model.
- (3)
- The influence of support component stiffness on the damping efficiency indicators of the structure is significant. After the variation of damper parameters, it is advisable to match the corresponding support component stiffness according to the specifications in order to obtain the true results of various damping efficiency indicators under optimal parameters. After matching the stiffness of the supporting members, the additional damping ratios in the case increased from 2.91% and 3.38% to 4.50% and 5.70%, respectively, representing an approximately 55% increase. Other damping efficiency indicators also showed significant improvement. This pattern is applicable to other frame shear wall structures with additional viscous dampers.
- (4)
- A simple and easy-to-use “damping design flowchart considering the impact of damper parameters on the damping efficiency” is proposed. By following the idea and method presented in this flowchart, designers can complete the damping design of other frame shear wall structures with additional viscous dampers. This flowchart can provide important guidance and reference for future designers in conducting damping design for frame shear wall structures.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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The First Set of Parameters | The Second Set of Parameters | ||||
---|---|---|---|---|---|
Serial Number | Damping Coefficient C | Damping Exponent α | Serial Number | Damping Coefficient C | Damping Exponent α |
1 | 60 | 0.15 | 1 | 20 | 0.25 |
2 | 60 | 0.25 | 2 | 40 | 0.25 |
3 | 60 | 0.35 | 3 | 60 | 0.25 |
4 | 60 | 0.45 | 4 | 80 | 0.25 |
5 | 60 | 0.55 | 5 | 100 | 0.25 |
6 | 60 | 0.65 | 6 | 120 | 0.25 |
Indicators | Response Surface Types | p | R2 |
---|---|---|---|
Additional damping ratio ξd | Poly2D | <0.0001 | 0.917 |
Reduction rate of vertex displacement μu | Poly2D | <0.0001 | 0.900 |
Reduction rate of base shear μV | Poly2D | <0.0001 | 0.901 |
Inter-story displacement utilization rate η | Plane | <0.0001 | 0.988 |
Damper force F/kN | Plane | <0.0001 | 0.970 |
Damper displacement u/mm | Plane | <0.0001 | 0.973 |
Indicators | X Direction | Y Direction |
---|---|---|
Additional damping ratio ξd | 2.91% | 3.38% |
Reduction rate of vertex displacement μu | 18% | 21% |
Reduction rate of base shear μV | 12% | 14% |
Inter-story displacement utilization rate η | 0.53 | 0.59 |
Damper force F/kN | 186 | 194 |
Damper displacement u/mm | 1.48 | 1.61 |
Indicators | X Direction | Y Direction |
---|---|---|
Additional damping ratio ξd | 4.50% | 5.70% |
Reduction rate of vertex displacement μu | 25% | 30% |
Reduction rate of base shear μV | 19% | 24% |
Inter-story displacement utilization rate η | 0.70 | 0.81 |
Damper force F/kN | 199 | 209 |
Damper displacement u/mm | 1.79 | 1.97 |
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Lan, X.; Wei, G.; Zhang, X. Study on the Influence and Optimization Design of Viscous Damper Parameters on the Damping Efficiency of Frame Shear Wall Structure. Buildings 2024, 14, 497. https://doi.org/10.3390/buildings14020497
Lan X, Wei G, Zhang X. Study on the Influence and Optimization Design of Viscous Damper Parameters on the Damping Efficiency of Frame Shear Wall Structure. Buildings. 2024; 14(2):497. https://doi.org/10.3390/buildings14020497
Chicago/Turabian StyleLan, Xiang, Guanglan Wei, and Xingxian Zhang. 2024. "Study on the Influence and Optimization Design of Viscous Damper Parameters on the Damping Efficiency of Frame Shear Wall Structure" Buildings 14, no. 2: 497. https://doi.org/10.3390/buildings14020497