## 6 Conclusions  
Notably, the vibration suppression efficiency of the TMD depends on structural frequency, and accurate simulation of pile-soil interaction is critical. The findings provide an economically viable and reliable solution for vibration-resistant design of deep-water jacket platforms under extreme marine conditions. Future research will focus on optimizing hybrid control strategies combining TMDs with fluid dampers. This study systematically evaluates the effectiveness of Tuned Mass Dampers (TMDs) in controlling the dynamic response of deep-water jacket platforms under typhoon and typhoon-wave loads through numerical simulations. The results indicate that TMDs demonstrate significant vibration reduction performance under both aligned and misaligned typhoon-wave load conditions.  
Under aligned load conditions, the TMD reduces the maximum displacements of the platform deck in the \(X\)-axis by 18.18%. The maximum velocities decrease by 13.33%, and the maximum accelerations are reduced by 26.19%. For base shear in the \(X\)-direction, the maximum value decreases by 17.71%. Under misaligned load conditions, the TMD shows more pronounced control over \(Y\)-direction displacement responses, with maximum displacement, velocity, and acceleration reductions of 20.00%, 19.05%, and 17.65%, respectively. Additionally, the maximum base shear decreases by 23.85%. The energy dissipation analysis demonstrates the effectiveness of the TMD in converting structural kinetic energy into heat through its damping mechanism under two conditions. The highest efficiency (68.2%) was observed in the \(Y\)-direction under misaligned load conditions.  
The experimental study on the frequency detuning sensitivity of the TMD reveals a key finding: the vibration suppression performance is significantly more sensitive to the stiffness deviation (\(\pm\)10%) than to the mass deviation (\(\pm\)10%). It is important to note that the quantitative mitigation performance presented in this study was obtained for a specific jacket platform design founded on a particular stratified seabed profile. The effectiveness of a TMD is sensitive to variations in platform geometry, water depth, and, crucially, the seabed stratigraphy that governs SSI. For significantly different platform configurations or site conditions, the TMD mass, stiffness, damping ratio, and potentially placementshould be re-optimized based on a site-specific dynamic analysis incorporating detailed SSI modeling, as performed in this study.  
Overall, the research results presented in this article provide an economically viable and reliable solution for the vibration-resistant design of deep-water jacket platforms under extreme marine conditions. Future research will focus on optimizing hybrid control strategies combining TMDs with fluid dampers.  
K.J.: Methodology: writing--original draft and visualization; G.Z.: Investigation, conceptualization, software, and writing--original draft; M.H.: Visualization, data curation, data analysis and interpretation; G.L.: Investigation, validation, and experimental design optimization; H.Y.: Investigation and writing--original draft; L.W. ([PERSON]) and [PERSON] ([PERSON]): Project administration and writing--review and editing. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (Grant No. 52409144) and the Zhejiang Provincial \"Pioneer\" R&D Program (Grant No. 2024C03031).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
Authors [PERSON], [PERSON] and [PERSON] were employed by the company ChinaPower China Huadong Engineering Corporation Limited. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.