# Study on Local Vibration Control of the 100 m X-BOW Polar Exploration Cruise Ship
## 1 Introduction
Since 1909, when [PERSON] first used TMD to control lateral tumbling vibrations in ships, TMD has been used extensively in the vibration control of ship structures and equipment [11]. [PERSON], [PERSON] [12] studied the effect of the mass ratio of TMD on the vertical vibration damping effect of steel plants and concluded that the damping effect of the plant with TMDs placed at the maximum response is better than that of the plant placed close to the excitation. [PERSON], [PERSON] [13] investigated the effect of pendulum tuned mass damper (PTMD) placed in the nacelle on the in-plane vibration response of Barge floating wind turbines and optimized the collision parameters. [PERSON], [PERSON] [14] investigated the effect of air-damped TMDs formed by replacing the oil damping in conventional tuned mass dampers with air damping on the vibration control of simply supported girder bridges under pedestrian loads. [PERSON], [PERSON], [PERSON], et al. [15] propose a tuned mass damper with negative stiffness using TMD applied to the vibration control of a propulsion shaft system, and provides a theoretical and design approach. The control effect of a tuned mass damper with negative stiffness was compared with that of a conventional tuned mass damper, and it was found that the control effect of a tuned mass damper with negative stiffness was 10 dB better than that of a conventional tuned mass damper. [PERSON], [PERSON], [PERSON] [16] propose a TMD using shape memory metals as dampers; a theoretical design method is provided in the paper, and it is used for wave-induced vibrations of jack-up marine platforms. At the same time, four calculation conditions were designed: 2-year regression period, 5-year regression period, 10-year regression period, and 100-year regression period. Based on the calculation results of the four conditions, it can be seen that the average reduction of vibration displacement of the platform reaches 43%. [PERSON], [PERSON], [PERSON], et al. [17] applied TMD to pipeline vibration control. Since the control band of a single TMD is narrow, multiple TMDs were installed on the pipeline in order to improve the control bandwidth, which was modeled and simulated using finite elements and compared experimentally; the method effectively improved the control bandwidth of TMDs. At present, TMD is mainly used for the overall vibration mode control, and there are few studies on the local vibration mode control. When the local vibration of hull structure occurs, it is generally the coupling of multiple local modes, and it is difficult to directly judge the participation degree of each local mode. When the 100 m X-BOW polar expedition cruise was in the commissioning or sea trial phase, tests revealed local structural vibrations at the sun deck on deck 7, but it was not possible to optimize the local structural adjustments at this time, so this paper proposes the use of a tuned mass damper (TMD) to control local structural vibration. TMD can be subsequently installed without extensive modification to the hull structure. The primary objective of this study is to introduce an innovative approach to control local structural vibrations on the 100 m X-BOW using TMDs. Our methodological contribution lies in the development of a local mode equivalent mass identification technique, which is crucial for the design of TMDs that target specific local modes within the mixed-mode vibration spectrum of the hull structure. This approach is significant as it allows for the effective control of vibrations in critical areas, such as the sun deck on deck 7, which was identified to have a local resonance frequency of 13.4 Hz during the commissioning phase.