## 1 Introduction
This device was installed not only to extend the lifespan of the propulsion system but also to reduce the emission of undesirable acoustic waves and to improve working conditions for the crew. As [PERSON] and [PERSON] [22] point out, the introduction of the damper was a breakthrough, as it significantly reduced vibration levels that could cause both technical issues (such as shaft fractures and bearing damage) and discomfort for personnel operating the vessel. [PERSON] [23] highlights that the experiences gained during work on submarines contributed to the further development of dampers used in various diesel engines, which later led to increased reliability in large marine propulsion systems. Meanwhile, [PERSON] and [PERSON] [24] emphasize that the use of viscous dampers was not only crucial for operational safety but also essential for the economical and comfortable operation of marine machinery by mitigating resonance phenomena and the risk of vibrations with amplitudes threatening the durability of the entire system. Although the issue of torsional vibration damping has a long history, it remains highly relevant today, as evidenced by numerous publications in recent years. [PERSON] and [PERSON] proposed a hybrid damping approach for optimizing torsional vibration dampers in cranktrain systems, improving system dynamics under varying operating conditions [25]. Similarly, [PERSON] et al. presented a comprehensive theoretical and application-based framework for designing torsional dampers tailored to diesel engines [26]. [PERSON] and [PERSON] introduced a torsional damper based on dilatant fluid, highlighting its suitability for four-stroke diesel engine crankshafts due to its adaptive viscosity behavior [27]. [PERSON] et al. investigated how marine operation conditions influence viscous damper characteristics in marine diesel engine shafting, revealing a direct impact on torsional vibration levels [28]. [PERSON] et al. described the design and deployment of torsional vibration dampers in field conditions, providing insights into their real-world application and reliability [29]. [PERSON] et al. applied physics-informed neural networks to adjust torsional damper models, achieving more accurate predictions of system behavior [30]. [PERSON] et al. reviewed both historical and emerging damping strategies in the vehicle industry, offering a broad perspective on current and future technologies for torsional vibration mitigation [31]. [PERSON] and [PERSON] [32] characterize the properties of a viscous torsional vibration damper filled with silicone oil, emphasizing mathematical modeling. Their work analyzes the crankshaft system dynamics and proposes vibration control methods based on the physical and rheological parameters of the damping medium. Meanwhile, [PERSON] et al. [33] examine the impact of silicone oil deficiency in a viscous torsional vibration damper on its damping performance. Their experimental results and theoretical analysis reveal how insufficient fluid levels affect damper functionality and the overall operational safety of the engine. [PERSON] et al. examined how the aging of silicone oil in dampers affects crankshaft vibration, underlining the importance of damping medium longevity in heavy-duty diesel engines [34]. [PERSON] et al. analyzed the heat dissipation performance of torsional vibration dampers, emphasizing its role in crankshaft durability and vibration control [4]. A related study by [PERSON] et al. focused on the optimization of silicone oil-based dampers for diesel generators, balancing thermal performance with damping efficiency [35]. Most recent studies have also addressed vibration damping, primarily focusing on longitudinal vibrations and the application of computational fluid dynamics (CFD) to analyze and optimize damping systems. For instance, [PERSON] et al. [36] conducted a numerical and experimental study on the damping performance of fluid viscous dampers, considering the gap effect, which is crucial for understanding the damping behavior in various dynamic systems. [PERSON] et al.