The embarrassingly parallel nature of the Bisection Algorithm makes it easy and efficient to program on a parallel computer, but with an expensive time cost when all symmetric tridiagonal eigenvalues are wanted. In addition, few methods can calculate a single eigenvalue in parallel for now, especially in a specific order. This paper solves the issue with a new approach that can parallelize the Bisection iteration. Some pseudocodes and numerical results are presented. It shows our algorithm reduces the time cost by more than 35–70% compared to the Bisection algorithm while maintaining its accuracy and flexibility.
Propeller-induced longitudinal vibration resonance in marine propulsion shafting systems causes great harm to the hull structure and is the primary source of shipboard noise. Integrating a friction damper with designed parameters into thrust bearings can prevent these issues. To investigate the performance of the damper-integrated thrust bearing in longitudinal vibration transmission control, an experimental and theoretical study is carried out in a laboratory-assembled test rig, which consists of components similar to the existing marine propulsion system. We developed a prototype of a thrust bearing designed with a friction-damping generation that allows switching from two supporting states, i.e., damper-connected and damper-disconnected states. Furthermore, a nonlinear analysis method for friction dampers is proposed. By this method, the way in which the friction damper changes the dynamic characteristics of the shafting system is analyzed. Based on the test rig, the acceleration frequency response function (AFRF) of the thrust bearing with and without a friction damper is measured. By comparison, the effectiveness of the friction damper is proved. The experimental results show that the friction damper suppresses the shafting longitudinal vibration response in a broadband frequency range and also confirms the stability of the damping effect, which does not change with the shafting rotational speed or static thrust from the propeller.
This paper presents a novel method for computing the symmetric tridiagonal eigenvectors, which is the modification of the widely used Inverse Iteration method. We construct the corresponding algorithm by a new one-step iteration method, a new reorthogonalization method with the general Q iteration and a significant modification when calculating severely clustered eigenvectors. The numerical results show that this method is competitive with other existing methods, especially when computing part eigenvectors or severely clustered ones.
The longitudinal vibration of the propulsion shaft system is a challenging issue for marine noise management. We conducted various static and dynamic tests on our built test rig for the shafting system, presenting the results in this paper. By combining experimental data and the particle swarm optimization algorithm, we identified the structural parameters that are difficult to obtain. With these parameters we establish a completed theoretical model of a shaft system containing branches, analyze how and why static thrust affects vibration, and give quantitative results of the force transmissibility. Our work provides a reference for subsequent researchers.
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