## 6 Results and Discussion
### Discussion
#### 6.2.2 Influence of W\({}_{\rm V}\):W\({}_{\rm A}\) on the Control Performance of the ISAMD
Figure 21 shows that the maximum displacements of the ISAMD are several times larger than those of the TMD. For example, with a frequency ratio of 2-4, the maximum displacements of the control mass block are roughly 4-6 times those of the TMD. The  
Figure 20: The average value of the maximum roof acceleration response ratio of the ISAMD, J5. large displacement responses of the control mass block restrict the application range of the ISAMD; it can only be installed in buildings with adequate space. 2.3 Seismic Resistance and Mass Block Displacement Influence of the ISAMD with Auxiliary Damper and Spring  
The large mass block displacement of the ISAMD is a major limitation of its application, as shown in Figure 21. Therefore, a feasibility study of the ISAMD with an auxiliary spring and damper installed to reduce the mass block displacement between the mass block and the structure was performed. The ISAMD in parallel with an auxiliary spring and damper is shown in Figure 22. The parameters of weight, added strength and damping coefficient interval of the ISAMD were \(\mathrm{W_{V}}\):\(\mathrm{W_{A}}=\omega_{0}:1,0,50,100\) and \(200\)-\(3600\)\(\mathrm{kN/m}\) and \(\mathrm{c_{a}}=0,20,\)\(40\)\(\ldots\)\(100\)\(\mathrm{kN}\)-\(\mathrm{s/m}\), respectively, to investigate the influence of seismic resistance and mass block displacement. The analysis of the control efficiency index J1 with the maximum displacement of the top floor showed that, when the stiffness of the auxiliary spring \(k_{aux}\) is much lower than the optimal stiffness of the TMD, J1 decreases as \(K_{aux}\) increases. When \(K_{aux}\) increases up to one-quarter of the optimal stiffness of the TMD, J1 increases as \(K_{aux}\) increases. Therefore, for  
Figure 16:0 The average value of displacement responses of the control mass block of the ISAMD, J6. Figure 16:1 ISAMD Structure with auxiliary spring and damper. the analysis example in this paper, the auxiliary spring stiffness of the ISAMD is 1/8-1/4 of the optimal stiffness of the TMD to effectively reduce the mass block displacement without reducing the shock absorption effect of the ISAMD displacement control. To facilitate the comparison of the influence of an auxiliary spring and damper on the control efficiency indices J1 and J5 and the mass displacement index J6, the average value of the average efficiency indices was defined as each index of the main spring frequency ratio of the ISAMD being between 2 and 3, \(W_{\text{V}}\):\(W_{\text{A}}=\omega_{0}:1\), the better parameter interval. Figure 16:2  
where _NCase_ is the number of analysis examples at which the frequency ratio of the ISAMD main spring is between 2 and 3. Figures 23-25 show the influence of the auxiliary spring and damper on the top displacement control index, top floor acceleration control index and mass block displacement control index, respectively. Figure 16:3 Influence of auxiliary spring and damper on the control index of maximal roof displacement. Figure 16:4 Influence of auxiliary spring and damper on control index of maximal roof acceleration. The bold black lines in Figures 23-25 show the variation of the control indices of the ISAMD with only the auxiliary spring. The conclusions from the observations can be drawn as follows:  
1. Figure 25 shows that, when the spring stiffness is up to 1000 \(\mathrm{kN/m}\), equivalent to one-quarter of the optimal stiffness of the TMD, the mass block displacement is reduced to twice that of the TMD. The displacement of mass blocks is effectively controlled with a reduction rate of about 60% compared to the original displacement reaction. 2. When the stiffness of the auxiliary spring is less than 1500 \(\mathrm{kN/m}\), the change in the displacement control effect for the maximum structural displacement reaction of the roof is less than 1%. 3. The auxiliary spring reduces the mass block displacement without affecting the control of structural acceleration; structural acceleration at the roof is even slightly lower than that without the auxiliary spring. 4.