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The propulsion shaft system of a ship is a critical component of the powertrain, subjected to direct contact between the shaft and bearing under various operating conditions, such as low speed, heavy load, and startup/shutdown phases. These conditions can lead to friction-induced vibrations and even result in issues such as flutter and noise. In this paper, a four-degree-of-freedom coupled model of the ship propulsion shaft system is developed on the basis of modal coupling theory to investigate the modal coupling phenomenon in detail. A combined complex modal analysis and the fourth-order Runge-Kutta method are applied to analyze modal coupling instability and identify the critical friction factor. The results indicate that the minimum critical friction coefficient is a crucial parameter influencing the stability of the system. The impact of both proportional and non-proportional damping conditions on the critical friction coefficient is examined. Furthermore, the effects of various damping parameters on the modal coupling instability of the system is summarized. These findings provide important theoretical support for vibration control and stability optimization in propulsion shaft systems, significant value for advancing theoretical models and optimizing practical engineering applications.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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