With the large-scale and complexity of ship propulsion shafting, it is more difficult to analyze and control the torsional vibration of shafting. Therefore, an effective control method for the torsional vibration of shafting is of great significance in the field of ship engineering. The main strategy of torsional vibration control adopted in this paper is to keep the natural frequency of a shaft system away from the excitation frequency through structural modifications. In addition, because the basic parameters of much of the equipment in engineering applications cannot be changed, this restriction cannot be ignored when seeking solutions related to structural modifications. This paper studies the partial eigenvalue assignment for the torsional vibration control of complex ship propulsion shafting using the gradient flow method, which can shift a “dangerous” natural frequency to a safe value, while satisfying complex physical constraints. The models of a ship propulsion system and a diesel generator set are established to demonstrate several different desired modification schemes and constraint conditions in practice. In particular, close frequencies are shifted. The numerical simulation results demonstrate that it is effective and feasible to make a partial frequency assignment of torsional vibration, which provides a reliable approach for the control of torsional vibration for complex shaft systems in practical engineering.

Electromagnetic vibration is an important excitation source for squirrel-cage induction motors. However, the electromagnetic vibration under various loadings has not been sufficiently analyzed. It is proposed in this paper that the electromagnetic vibration of motors under different loads can be obtained by analyzing the amplitude of the electromagnetic force wave. The Maxwell tensor method is employed to derive the spatial and temporal distributions of the radial force. This paper also calculates the radial force using the finite element method and decodes the calculated results using two dimensional fast Fourier transform (2D-FFT) to determine the amplitude of the electromagnetic force at the spatial order under different loads. In addition, through the modal analysis of the stator core, it can be concluded that in the case of nonresonance, the vibration response increases when the electromagnetic force of the first-order and second-order rotor slot harmonic increases. Finally, the conclusion is verified by separating the electromagnetic vibration of the motor using a vibration test rig.