# Study on Local Vibration Control of the 100 m X-BOW Polar Exploration Cruise Ship
## 4 Conclusions  
According to the global mode equivalent mass solution method and the spatial destruction principle of local mode mass, a solution method of single local mode equivalent mass in mixed modes is proposed, and the single local mode equivalent mass of the seventh-layer sun deck in the 100 m X-Bow polar exploration cruise ship is solved by using this method.  
The finite element model of the 100 m X-Bow polar cruise ship was established to predict the structural vibration response. Six typical cabins were selected, and the simulation value of the vibration response of these six cabins was compared with the test value. The frequency response curve trend was basically the same, and the effective value error of the vibration response was within 22%, but the difference was only 0.24 mm/s. In the authors' opinion, the error can be ignored. So, the simulation results meet the engineering accuracy requirements and verify the effectiveness of the model, which can be used for vibration control analysis.  
The main excitation frequency was determined to be 12.5 Hz. Based on this frequency, the local mode search of the whole ship model was carried out, and the search range was 11.25-13.75 Hz. Finally, the natural frequency of the seventh-layer sun deck was determined to be in the range of 11.25-13.75 Hz, which was consistent with the propeller excitation blade frequency, and there was a resonance risk. This area is the area with the largest test response, and the vibration speed is 1.07 mm/s. It is necessary to control the vibration in this area.  
Figure 12: Control effect at 18.8 Hz.  
Figure 13: Comparison of responses before and after TMD control on the seventh sun deck.  
Using the local mode equivalent mass solution method, the local equivalent mass of the seventh layer of the sun deck is solved. The mass ratio \(\mu\) is set as 0.005, 0.01, 0.02, 0.05, 0.1, and 0.2. According to the six mass ratios, the six optimal parameters of TMD are determined. The optimal mass ratio of TMD in this region is determined to be 0.05. When the mass ratio of TMD is 0.05, the TMD has the vibration absorption effect of 31 dB at 13.4 Hz, and the amplitude responses at 10 Hz and 18.8 Hz also have certain control effects, which are 3 dB and 2 dB, respectively. The overall control frequency band is flat, and the robustness is good. After TMD was installed on the model loaded with the excitation source, the response around 13.4 Hz decreased from 0.8 mm/s to 0.13 mm/, indicating that TMD has a good control effect.  
In summary, this study not only enhanced the understanding of local vibration control for polar exploration cruise ships but also effectively reduced the vibration levels in key areas by applying TMD technology, thereby improving the safety and comfort of the vessel. This work demonstrates that significant improvements in the vibration control effectiveness of ship structures can be achieved through precise modal analysis and parameter optimization, which has important practical application value for ship design and operational maintenance.  
Methodology, [PERSON]; Software, J.C. and G.W.; Validation, G.W.; Data curation, H.G.; Writing--original draft, J.C.; Writing--review & editing, H.G.; Visualization, Z.L.; Supervision, [PERSON] All authors have read and agreed to the published version of the manuscript.  
The authors disclose receipt of the following financial support for the research, authorship, and/or publication of this article: this work was supported by the Science & Technology Commission of Shanghai Municipality and Shanghai Engineering Research Center of Ship Intelligent Maintenance and Energy Efficiency (Grant No. 20 DZ2252300) and Shanghai Maritime University.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest regarding the publication of this paper.