## 5 Dynamic Loading Mitigation of Offshore Platform Using TMD
### Dynamic Responses and Discussion
#### 5.2.2. Misaligned Typhoon and Typhoon-Wave  
Figures 14-16 systematically illustrate the time-domain and frequency-domain responses of acceleration, velocity, and displacement in the \(X\)- and \(Y\)-axis directions for the DTMD and Initial Design (ID) under misaligned typhoon and w  
Figure 12: Deck acceleration under aligned typhoon and typhoon-wave. (**a**) Time-domain simulation results in the \(X\)-axis direction; (**b**) Frequency-domain simulation results in the \(X\)-axis direction; (**c**) Time-domain simulation results in the \(Y\)-axis direction.  
Figure 13: Base shear forces under aligned typhoon and typhoon-wave. (**a**) Time-domain simulation results in the \(X\)-axis direction; (**b**) Frequency-domain simulation results in the \(X\)-axis direction; (**c**) Time-domain simulation results in the \(Y\)-axis direction; (**d**) Frequency-domain simulation results in the \(Y\)-axis direction.  
the \(X\)-axis direction, the peak values of displacement, velocity, and acceleration in the time domain are 0.17 m, 0.58 m/s, and 0.75 m/s\({}^{2}\), respectively. For the DTMD, the corresponding values are 0.14 m, 0.49 m/s, and 0.54 m/s\({}^{2}\), representing reductions of 17.65%, 15.52%, and 28.00%, respectively. In the \(Y\)-axis direction, the peak values of displacement, velocity, and acceleration in the time domain are 0.30 m, 0.84 m/s, and 0.85 m/s\({}^{2}\), respectively. For the DTMD, the corresponding values are 0.24 m, 0.68 m/s, and 0.70 m/s\({}^{2}\), representing reductions of 20.00%, 19.05%, and 17.65%, respectively. In both the \(X\)-axis and \(Y\)-axis directions, the displacement and velocity responses exhibit multiple distinct peaks within the low-frequency range, while the acceleration response demonstrates predominant spectral energy concentration within the same frequency band. The implemented TMD significantly mitigates the low-frequency peaks in acceleration and achieves additional reduction in the peaks of displacement and velocity responses. The energy dissipation efficiency for this condition is 59.8% in the \(X\)-direction and 68.2% in the \(Y\)-direction.  
Figure 17 illustrates the influence of the TMD on the base shear at the leg bottom under misaligned typhoon-wave load conditions. In the \(X\)-axis direction, the maximum and minimum base shear values for the IDD are 2431.9 kN and \(-\)279.6 kN, respectively, while the corresponding values for the DTMD are 1865.5 kN and \(-\)142.1 kN, representing reductions of 23.29% and increases of 49.17%, respectively. In the \(Y\)-axis direction, the absolute maximum and minimum base shear values for the IDD are 269.2 kN and \(-\)59.0 kN, respectively, whereas the DTMD values are 205.0 kN and \(-\)46.3 kN, showing reductions of 23.85% and increases of 21.53%, respectively. Spectral analysis of the shear force reveals that energy in both \(X\)- and \(Y\)-axis directions is predominantly concentrated within the low-frequency range of 0-0.2 Hz, where the TMD achieves significant peak attenuation.  
Figure 14: Deck displacement under a misaligned typhoon and typhoon wave. (**a**) Time-domain simulation results in the \(X\)-axis direction; (**b**) Frequency-domain simulation results in the \(X\)-axis direction; (**c**) Time-domain simulation results in the \(Y\)-axis direction; (**d**) Frequency-domain simulation results in the \(Y\)-axis direction.  
Figure 16: Deck acceleration under a misaligned typhoon and typhoon-wave. (**a**) Time-domain simulation results in the \(X\)-axis direction; (**b**) Frequency-domain simulation results in the \(Y\)-axis direction; (**d**) Frequency-domain simulation results in the \(Y\)-axis direction.  
Figure 15: Deck velocity under a misaligned typhoon and typhoon-wave. (**a**) Time-domain simulation results in the \(X\)-axis direction; (**b**) Frequency-domain simulation results in the \(X\)-axis direction; (**c**) Time-domain simulation results in the \(Y\)-axis direction; (**d**) Frequency-domain simulation results in the \(Y\)-axis direction.