# The Influence of Chamfered and Rounded Corners on Vortex-Induced Vibration of Super-Tall Buildings
## 5 A Brief Analysis of the VIV Reduction Mechanism  
As mentioned above, many researchers have studied the wind load of super high-rise buildings with different chamfer ratios based on synchronous pressure tests and high-frequency force balance tests. This paper does not repeat such tests but uses previous test data to assist the analysis of this study. Figure 8 shows the comparison between the crosswind base bending moment of the static model and the wind-induced response of the aeroelastic model in this paper, in which the base bending moment is obtained by [PERSON] through the force balance test [19]. The data in Figure 8 are normalized results, i.e., both the wind-induced bending moment and displacement of the non-chamfer are set to 1. Figure 7: \(St\) number of chamfer model by existing studies [3; 17; 18; 20]. It can be seen from Figure 8 that:  
1. When \(V_{r}\) is smaller than \(V_{c}\) (\(V_{r}\) = 7.0, \(V_{r}\) = 8.0, etc. ), the normalized wind-induced response is consistent with the results of the normalized bending moment, and both of them gradually decrease with the increase in chamfer ratio. When the chamfer ratio reaches 7.5%, the normalized bending moment and wind-induced response reach the minimum, and the decrease is about 25% compared to the non-chamfer model;
2. When \(V_{r}\) is close to \(V_{c}\) (\(V_{r}\) = 10.0, \(V_{r}\) = 10.5, etc. ), the normalized wind-induced response is very different from the normalized bending moment. With the increase of the chamfer ratio, the wind-induced response decreases significantly faster than that of the base bending moment. When the chamfer ratio is equal to 7.5%, the decrease of wind-induced response reaches 70%, which is much greater than that of base bending moment (25%);
3. The vibration reduction effect is not always positively correlated with the chamfer ratio. When the chamfer ratio is larger than 7.5% (\(R_{c}\) = 10%, \(R_{c}\) = 12.5%, etc. ), the normalized wind load and response rebound to some extent. In order to analyze the VIV reduction mechanism from the perspective of aeroelastic effects, the aerodynamic damping ratio of the aeroelastic model is calculated by using the random decrement technique. The random decrement technique is widely used to evaluate aerodynamic damping ratios from random vibration responses of structures [27; 28; 29]. In the process of the random decrement technique used in this paper, the bandwidth band pass filter is [\(n_{1}(1-20\%)\), \(n_{1}(1+20\%)\)], and the time length of the data sample is 100 s. The amplitude of the signal intereception is \(\sigma_{y}\) with an error range of 5%. On the basis of the random decrement technique, free attenuation curves can be obtained through time histories of tip displacement. The exponential decay rate (total damping (\(\xi_{t}\))) could be identified by the envelope of random decrement signatures, and the aerodynamic damping ratio (\(\xi_{a}\)) could then be calculated by Equation (4). \[\xi_{a}=\xi_{t}-\xi_{s} \tag{4}\]  
where the subscript \(a\), \(t\), and \(s\) denote aerodynamic, total, and structural, respectively. Figure 9 shows the aerodynamic damping results of the models with different chamfer ratios. It can be seen from Figure 9 that:  
1. When the chamfer ratio is 2.5%, the aerodynamic damping is consistent with that of the non-chamfer model, and there is a significant negative aerodynamic damping phenomenon when \(V_{r}\) is close to \(V_{c}\). 2. When the chamfer ratio increases to 5%, the negative aerodynamic damping phenomenon disappears. Obviously, this result of the aerodynamic damping ratio is closely related to the wind-induced response. Figure 8: Normalized wind-induced response and bending moment: (**a**) normalized RMS responses; (**b**) normalized bending moment [19]. The above analysis shows that the reduction of crosswind response is mainly caused by the reduction of wind load when the \(V_{r}\) is small.