# PTMD Control on a Benchmark TV Tower under Earthquake and Wind Load Excitations
## 6 Vibration Control with PTMD
### Wind Load Excitation Cases  
Time domain analyses are employed to calculate the responses of the structure under typical typhoons and stochastic wind loads. In typhoon cases, the time history of the wind speed is selected from the record of an anemometer installed on the Canton Tower. Typical recorded wind speeds and wind angle data are shown in Figure 7. It is assumed that wind load only acts on each node along the long and short axes. Information about the shape coefficient is used to generate the wind load from the wind speed, and is collected from the wind tunnel experiments done by Tongji University, China. The approximate windward area of each section is derived from the full-order FE model of the structure. After generating, the wind load will be decomposed into two directions, along the long-axis and short-axis, respectively. The composition force along the two directions will then be calculated and applied to the corresponding nodes of the reduced order model. For simplification, it is assumed that the segment between two adjacent nodes share the same wind load value. The time-history displacement and acceleration responses of the uncontrolled, TMD-controlled, and PTMD-controlled systems are shown in Figure 8. A summary of the peak and RMS responses on the mast top and the tower top of the structure are listed in Tables 3 and 4. In these cases, the weight of the mass is fixed as 300 t for comparison. It should be noted that, as shown in Figure 8b, even though the wind excitation can be quite severe, the PTMD did not contribute much vibration mitigation. The reason for the lack of vibration suppression can be seen in Figure 8c, where one can see that the bounding force  
Under typhoon excitation, it is shown that the proposed PTMD shares similar control effectiveness; only slight improvement is noticed on the peak and the RMS values. It can be observed from the tables that both control approaches can reduce the peak and RMS responses. On the mast top, the peak displacement responses are reduced by 19.14% and 34.75% subjected to Typhoon Haima and Typhoon Nanmado excitations, respectively, and the RMS displacement responses are reduced by 21.50% and 33.23%. Meanwhile, the peak displacement response along the \(y\)-direction on top of the mast are reduced by 24.24% and 32.86% under these typhoon excitations. When it comes to the acceleration responses, 18.46% and 28.15% control effectiveness values are obtained for peak responses on top of the mast, and 30.84% and 32.53% for the reduction of the RMS responses. As listed in the table, the  
Figure 8: Time-history responses under Typhoon Haima excitation (2011). PTMD is able to reduce the peak displacement responses on top of the main tower by 24.23% and 20.72%, but it is also important to notice that the peak acceleration responses along the short axis on the tower top are slightly increased when the TMD or PTMD is installed. Stochastic wind load is generated from the Davenport spectrum to further verify the effectiveness of the devices. The AR method is utilized here for stochastic wind load generation. The time-history of the generated wind speed and the responses along the long-axis on the tower top and mast top are shown Figures 9 and 10 and Table 5. The PTMD still observed similar control efficiency, not much better than that of the TMD, but the control efficiency is better than the typhoon excitation cases. Both of them are capable of reducing the peak and RMS responses by 57.79% and 49.65%, respectively.