# Wind-Induced Response Control of High-Rise Buildings Using Inerter-Based Vibration Absorbers
## 4 Wind-Induced Response Mitigation Using Inerter-Based Vibration Absorbers
### Effects of the Inerter-Based Vibration Absorbers on Wind-Induced Accelerations  
Excessive wind-induced acceleration response may cause discomfort to building occupants and poses serious serviceability issues [66]. Wind-induced accelerations of the benchmark 340 m tall building, together with the TMD-, TMDI- and the TID-equipped building, are analyzed for a 33.86 m/s wind speed (10-years return period related to serviceability limit state) for each of the 24 wind directions. Figure 16 illustrates a segment of the top-floor time-history acceleration response (for an overall duration of 20 min) corresponding to 90\({}^{\circ}\) wind direction. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Selected Condition** &
\begin{tabular}{c} **Wind** \\ **Direction (\({}^{\circ}\))** \\ \end{tabular} & \(\mathbf{u_{\text{OS}}^{top}}\)**(m)** & \(\mathbf{u_{\text{TMDI}}^{top}}\)**(m)** & \(\mathbf{u_{\text{TIDI}}^{top}}\)**(m)** & \(\mathbf{F_{\text{VA}}^{(\text{TMDI})}}\) & \(\mathbf{F_{\text{va}}^{(\text{TIDI})}}\) & \(\mathbf{F_{\text{va}}^{(\text{TIDI})}}\) \\ \hline Minimum \(F_{uu}\) (TMDI) & 330 & \(-\)0.1608 & \(-\)0.1438 & \(-\)0.1438 & \(-\)0.1416 & 10.56 & 10.52 & 11.94 \\ Maximum \(F_{uu}\) (TMDI) & 90 & 0.2293 & 0.1513 & 0.1519 & 0.1421 & 34.01 & 33.74 & 38.02 \\ Minimum \(F_{uu}\) (TID) & 330 & \(-\)0.1608 & \(-\)0.1438 & \(-\)0.1438 & \(-\)0.1416 & 10.56 & 10.52 & 11.94 \\ Maximum \(F_{uu}\) (TID) & 90 & 0.2293 & 0.1513 & 0.1519 & 0.1421 & 34.01 & 33.74 & 38.02 \\ Max positive displacement OS & 90 & 0.2293 & 0.1560 & 0.1519 & 0.1421 & 34.01 & 33.74 & 38.02 \\ Max negative displacement OS & 75 & \(-\)0.2130 & \(-\)0.1476 & \(-\)0.1482 & \(-\)0.1404 & 30.71 & 30.44 & 34.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Vibration-mitigation effects in terms of top-floor displacement response for some loading configurations. Following time histories of acceleration response, extreme acceleration responses can be obtained in terms of RMS value. Figure 17 presents variation of extreme acceleration responses along the building height corresponding to three typical wind directions, namely 0\({}^{\circ}\), 45\({}^{\circ}\) and 90\({}^{\circ}\) wind directions. Figure 17 demonstrates that TMD, TMDI and TID have significant vibration absorbing effects on wind-induced acceleration response. In general, the vibration-mitigation effects of the TID are better than those of the TMD and TMDI, especially for wind direction of 45\({}^{\circ}\). As stated previously, the three vibration absorbers share the same physical mass ratio. The vibration-mitigation effects are not only related to the parameters of TMD, TMDI or TID, but also depend on the predominant frequency components of aerodynamic forces. At 0\({}^{\circ}\) and 90\({}^{\circ}\) wind direction (cf. Figure 17a,c) the acceleration response at the \(x\)-axis are mainly induced by incoming turbulence flow and vortex shedding effects, respectively. At 45\({}^{\circ}\) wind direction, the acceleration response at the \(x\)-axis is affected by a combination of incoming turbulence flow and vortex shedding. Hence, it can be concluded that the vibration mitigation effects of TID is the best among three vibration absorbers, and the performance of TMDI is better than that of TMD for specific wind direction of 45\({}^{\circ}\). Figure 16: Time histories of acceleration at the 69 th story along the \(x\)-axis corresponding to 90\({}^{\circ}\) wind direction. Figure 17: _Cont._  
Figure 18 shows the variation of extreme top-floor accelerations corresponding to a variety of wind directions ranging from 0\({}^{\circ}\) to 345\({}^{\circ}\). From Figure 18 we can see that TMD, TMDI and TID significantly control extreme acceleration responses, especially at 45\({}^{\circ}\) wind direction. For this wind direction, the response decreased from 0.0687 m/s\({}^{2}\) (original structure) to 0.0307 m/s\({}^{2}\) (TID-equipped structure).