###### Abstract
[18; 19; 20] introduced the ShaftDesigner shaft system calculation software in detail, used this software to establish a 3D model of the shaft system based on the shaft system layout data, and used the model for frequency domain torsional vibration calculation and time domain transient response calculation. [PERSON], [PERSON] [21] used Hypermesh and MSC Nastran software for joint simulation analysis, established a three-dimensional finite element model of the shaft system, and used the model to perform longitudinal and torsional coupled vibration calculations of the shaft system, analyzing the excitation and damping loading of the finite element. [PERSON], [PERSON] et al. [22] analyzed the vibration power flow behavior of the coupled beam in the mid-frequency band through the mixed finite element method. [PERSON], [PERSON] et al. [23; 24] studied the dynamic stability of the torsional vibration of the shaft system connected by [PERSON]'s joints through the continuous system model and regarded the shaft system as a continuous (distributed parameter) system using the finite element method. The energy method for undamped vibration systems considers the sum of the system's kinetic energy and potential energy at any moment to be equal; for damped forced vibration systems, it considers the energy input by the excitation force to the system to be equal to the work consumed by the damping of all parts of the system. [PERSON], [PERSON] et al. [25; 26] proposed two simplified methods based on the calculation of the torsional vibration of the ship's power transmission system, which was verified by experiments, and further corrected the damping coefficient. [PERSON], [PERSON] et al. [27] employ an energy method in conjunction with the amplification factor method, integrated with the supergraph method, and a comprehensive method for torsional vibration shafts to address the torsional vibration issues of discrete-continuous mechatronic systems. [PERSON], [PERSON] et al. [28; 29; 30] analogized the propulsion shaft system to a Jeffcott rotor, developed an experimental unit to simulate longitudinal and torsional coupled vibration, and conducted vibration experiments on it to verify its theoretical principles. In the field of dynamic response analysis of ship propulsion shaft systems, numerous scholars have constructed corresponding ship propulsion shaft system dynamic models. They have conducted in-depth analyses of the dynamic characteristics of propulsion shaft systems under the influence of different excitation loads and their influencing parameters, based on various research methodologies and boundary conditions. However, studies on propulsion shaft systems incorporating shaft-driven generators without bearing support are relatively scarce, particularly regarding the discussion of dynamic torque characteristics. This paper presents a systematic study on this \"new type\" of propulsion shaft system with a shaft-driven generator without bearing support, analyzing the dynamic torque characteristics of the propulsion shaft system under conditions with and without the generator load connected, as well as the vibration characteristics and load distribution of the shaft system. Furthermore, the theoretical analysis is validated through actual ship experiments, and the findings of this study hold significant importance for engineering practice. The remainder of this paper is organized as follows: In Section 2, the consistency between the simplified mathematical model of the propulsion shafting system and the actual physical model is discussed, along with the study of the time domain dynamic response calculation method for the propulsion shafting system. In Section 3, taking a 16000 TEU container ship as an example, dynamic response simulation calculations for the propulsion shafting system are conducted, and the vibration torque and stress of each unit equipment are analyzed to identify the resonant speed points.