## 5 MTMD Applications on Taizhou Bridge
### Parametric Analysis on the MTMD Application
#### 5.4.4 Frequency Band Width Ratio  
The control efficiency of the lateral and vertical MTMD systems is investigated with different frequency bandwidth ratios, as shown in Figure 18. During the process, the other updated parameters are \(\mathbf{N}=13\), \(\mathbf{\mu}=0.03\), \(\zeta_{0}=2\%\) for the lateral MTMD and \(\mathbf{N}=11\), \(\mathbf{\mu}=0.02\), \(\zeta_{0}=2\%\) for the vertical MTMD.  
According to Figure 18, a typical feature in the parametric analysis is that the control efficiency first increases to a peak and then decreases with the augment of the frequency bandwidth ratio. When the frequency bandwidth ratio is small, the effective frequencies that can be controlled are limited. An extreme case is that, when the frequency bandwidth ratio is zero, the MTMD is reduced to the TMD, which means only the central frequency is determined as the controlled target. Hence, with the increase of the frequency bandwidth ratio, the control efficiency of the MTMD will have a prominent improvement, but when the frequency bandwidth ratio becomes larger, the frequency difference between two adjacent TMDs is increasing. This will lead to the same problem resulting from the case with small number of TMDs. In such a status, only limited discrete frequencies can be controlled by the MTMD system, which accounts for the decreasing attenuation factor in the high frequency bandwidth range.  
The robustness of the MTMD system is also investigated via changing the frequency ratio, which is also shown in Figure 18. In this study, there is a 10% maximum frequency shifting to the central frequency considered. For the lateral MTMD, the control efficiencies in the five cases do not deviate too much from each other. However, for the vertical MTMD, the performance is sensitive to the frequency variation in the range of small frequency bandwidth ratios. This phenomenon can be obviously alleviated utilizing high frequency bandwidth ratios. The lateral buffeting responses are dominated by two modes, which means the buffeting responses cannot be well mitigated in the  
Figure 18: Influence of the frequency bandwidth ratio on the control efficiency of MTMD: (**a**) Lateral cases; (**b**) Vertical case.  
cases with low frequency bandwidth ratios as the central frequency is between the frequencies of the two modes. That is why the performance of the MTMD sensitive to frequency variations in low frequency-bandwidth-ratio cases is not captured in the lateral MTMD.  
For the lateral MTMD, the frequency bandwidth ratio should cover the two dominant modes. To'make the control efficiency of the MTMD sufficiently performed, the preferred value of the frequency bandwidth ratio for the lateral MTMD is determined as 0.5. When the frequency bandwidth ratio is 0.3, the control efficiency of the vertical MTMD is only a little smaller than the peak value, but the robustness is obviously improved and can be accepted for application. Hence, the preferred value of the frequency bandwidth ratio is updated as 0.3 for the vertical MTMD.  
In this study, the prescribed thresholds for the control efficiencies of the lateral and vertical MTMD systems are both set as 20%. Thus, with only one round, the main parameters of the MTMD systems for the buffeting control of Taizhou Bridge are determined via the step-updating framework. Of course, a better attenuation factor can be obtained after another step or two, but the increment would not be as big as the first step due to the small gradient observed in the parametric analysis. The preferred values for the design parameters of the MTMDs are presented in Table 3.