In this paper, flexural vibration and power flow transmission of a ship propulsion shafting structure are analyzed via energy principle description in conjunction with Rayleigh–Ritz procedure, in which the shafting vibration displacement is constructed as a superposition of Fourier series and boundary-smoothing supplementary functions. Effect of the distributed bearing support and thrust loading of propulsion shafting system is considered in terms of potential energy of system Lagrangian. Numerical examples are presented to demonstrate the reliability and effectiveness of the established model by comparing results with those from finite element method. Results show that the current model can deal with the vibration analysis of ship propulsion shafting with thrust loading and distributed bearing very well. Influence of boundary restraints, stiffness of distributed bearings, and thrust loading on vibration characteristics of ship shafting system is studied and addressed. Numerical study on power flow analysis is also conducted to investigate the characteristics of vibrational energy transmission in such practical structure. Results show that the stiffness of spatial bearing support has significant influence on vibrational energy transmission and thrust force will greatly affect the total input power into such structure.

中文翻译：

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具有一般支撑和推力载荷的船舶推进轴系的振动特性和功率流分析

本文结合能量原理描述和Rayleigh-Ritz程序，分析了船舶推进轴系结构的挠曲振动和动力传递，其中轴系振动位移构造为傅立叶级数和边界平滑辅助函数的叠加。根据系统拉格朗日的势能，考虑了分布式轴承支撑和推进轴系推力载荷的影响。数值算例通过与有限元方法的比较，证明了所建立模型的可靠性和有效性。结果表明，该模型能够很好地处理推力载荷和分布轴承情况下的船舶推进轴系的振动分析。边界限制的影响，研究并解决了分布式轴承的刚度，推力载荷对船舶轴系振动特性的影响。还对潮流分析进行了数值研究，以研究这种实用结构中振动能量传递的特性。结果表明，空间轴承支架的刚度对振动能量的传递有很大的影响，推力将极大地影响这种结构的总输入功率。