# Wind-Induced Response Control of High-Rise Buildings Using Inerter-Based Vibration Absorbers
## 5 Conclusions  
The wind-induced response of a benchmark 340 m tall building equipped with inerter-based vibration absorber, i.e., TMDI and TID, has been investigated. The analysis has been carried out in the time-domain, by considering the time histories of aerodynamic forces computed from synchronous multi-point pressure measurements in wind tunnel tests, which accounts for the actual cross section of the building and the existing surrounding conditions. The results have been analyzed in terms of wind-induced displacement and acceleration response as well as ESWLs on the original structure, and comparatively on the building equipped with the TMD, TMDI and TID corresponding to 24 different wind directions (from 0\({}^{\circ}\) to 345\({}^{\circ}\) at an interval of 15\({}^{\circ}\)). The main contents and findings of the present work are summarized as follows:  
1. Displacement- and acceleration-based optimizations have been performed to obtain the best parameters of the TMD, TMDI and TID in a 3D design space, including the installation floor, the frequency ratio and the damping ratio as explicit design variables. The proposed procedure attempts to find a good trade-off between displacement mitigation and acceleration mitigation, considering results from a constrained optimization problem in which the installation floor represents a design variable being incorporated in the optimization procedure;
2. Both wind-induced extreme top-floor displacement and acceleration responses of the benchmark building can be effectively mitigated by the TMDI and TID. Among the three vibration absorbers, the TID outperforms the TMDI and the TMD, and the acceleration mitigation effect of the TMDI is better than that of the TMD. The extreme displacement and acceleration response of the original structure are 0.2293 m and 0.1232 m/s\({}^{2}\), respectively. The installation of the TMDI has reduced these response values to 0.1519 m and 0.0685 m/s\({}^{2}\), respectively, with a resulting factor of vibration absorbing \(F_{\text{rot}}\) equal to 33.74% and 44.40%, respectively. The best vibration mitigation effect is achieved by the TID, which reduces the extreme displacement and acceleration to 0.1421 m and 0.0602 m/s\({}^{2}\), respectively, corresponding to \(F_{\text{rot}}\) of 38.02% and 51.12%, respectively;
3. Comparison among the three different vibration absorbers has shown that the TID with same physical mass ratio as the TMD and TMDI can achieve better vibration mitigation effects in terms of displacement and acceleration responses. In particular, the factors of vibration absorbing \(F_{\text{rot}}\) of TMD, TMDI and TID for extreme displacement have been 34.01%, 33.74% and 38.02%, respectively, and the analogous factors for extreme acceleration have been 43.04%, 44.40% and 51.12%, respectively. The performance of TID slightly outperforms the other two vibration  
Figure 19: Variation of ESWLs along the building height corresponding to two wind directions: (**a**) 0\({}^{\circ}\) wind direction; (**b**) 45\({}^{\circ}\) wind direction. absorbers in terms of mitigating ESWLs, which is consistent with the results of displacement mitigation effect;
4. Optimizations of parameters have demonstrated that the TMDI and TID achieve the best vibration mitigation effects when the first terminal is not installed at the top floor, but at the mid-upper place of the primary structure with TMDI/TID topologies such that the inerter spans four stories. In this configuration, the TID can achieve better wind-induced vibration mitigation than the TMD employing the same physical mass ratio as that of the corresponding TMD (thus implying a significant reduction in terms of physical mass actually allocated due to the mass-amplification effect of the inerter when the TID scheme is designed to achieve the same vibration mitigation effect as that of TMD);
5.