###### Abstract  
The propulsion shaft system, as the core of the ship's power system, has attracted widespread attention in terms of vibration. This paper is dedicated to the study of the dynamic response characteristics of the ship propulsion shafting system, with a particular focus on the impact of the shaft-driven generator supported by bearings on the dynamic torque of the shafting system. A classic lumped-parameter equivalent system model is adopted, and the time domain transient response simulation calculation is conducted based on the Newmark-\(\beta\) method. A comprehensive analysis is made of the vibration torque and vibration stress in the propulsion shaft system under different rotational speeds and working conditions, with or without the shaft-driven generator connected to the load. Dynamic vibration torque measurements are also taken on a 16100 TEU ship for the propulsion shaft system to analyze the consistency between simulation results and experimental results. The results show that at the rated speed of the main engine at 80 rpm and adjacent speeds, the error between the simulation calculation results and the actual measured torque results at the pre- and post-motor measurement points is less than 10% and is much less than the continuous allowable torque of 4.01 \(\times\) 10\({}^{6}\) N-m and the instantaneous torque. This installation state, including the propulsion shaft system with the shaft-driven generator supported by bearings, can safely navigate during normal operation. This provides theoretical and experimental support for the future installation of the propulsion shaft system with the shaft-driven generator supported by bearings. In addition, the actual ship experiment enhances the universality and reliability of the research. propulsion shafting; dynamic response; vibration torque; vibration stress Vol. 0, No. and its connected components under various operating conditions, ensuring the integrity and safety of the structure. This is vital for subsequent ship design and operation to ensure that the ship meets its predetermined performance requirements. Particularly for the \"new type\" of propulsion shaft system that includes a shaft-driven generator without bearing support, the engagement and disengagement of the generator's load may lead to fluctuations in dynamic torque along the shaft system, thereby affecting the load distribution, vibration characteristics, and overall stability of the shaft system. Additionally, changes in the load of the shaft-driven generator may cause shifts in the stress distribution within the shaft system, with excessive stress potentially leading to structural fatigue or damage. Consequently, conducting simulation calculations and experimental analyses to study the dynamic response characteristics of the propulsion shaft system with a shaft-driven generator without bearing support and to predict its vibration characteristics holds significant engineering importance. The system matrix method is a crucial computational technique for determining the dynamic response of propulsion shafting systems. It involves solving the characteristic equations of homogeneous differential equation sets using methods such as the QR algorithm and the Jacobi method for free vibration calculations. Additionally, it employs techniques like Gaussian elimination to solve non-homogeneous differential equation sets for dynamic response analysis. [PERSON] et al. [1] conducted a frequency domain analysis of the propulsion shafting system using the system matrix method and used the Newmark method to simulate the transient torsional vibration caused by the slip of the clutch between the shaft generator and the speed increase gearbox in a four-stroke diesel engine shaft system. [PERSON], [PERSON] et al. [2] utilized the system matrix method, incorporating an enhanced Kalman filter to estimate the excitation and torque response of the propeller and motor based on the system's dynamic model and measured data.