Vibration Characteristics and Power Flow Analyses of a Ship Propulsion Shafting System with General Support and Thrust Loading

Abstract

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.

Transverse forced nonlinear vibration analysis of a double-beam system with a supporting nonlinearity

“…in which, ψ 1m (x 1 ) and ψ 2n (x 2 ) is the m th and n th weight function of Beam I and Beam II (m = 1, 2, … M and n = 1, 2, …, N). For this investigation, mode functions of the single-beam structure without the coupling element, concentrated mass, viscous damping, and nonlinear support are regarded as the trail and weight functions, which can be accurately obtained according to the method applied in the reference (Xu et al, 2020). By putting the terms linked to the consequent derivate of time into one side, equation ( 12) can be rederived as,…”

“…By utilizing the Galerkin discretization condition, the residual equations of such a double-beam system are derived asandin which, ψ 1 m ( x 1 ) and ψ 2 n ( x 2 ) is the m th and n th weight function of Beam I and Beam II ( m = 1, 2, … M and n = 1, 2, …, N). For this investigation, mode functions of the single-beam structure without the coupling element, concentrated mass, viscous damping, and nonlinear support are regarded as the trail and weight functions, which can be accurately obtained according to the method applied in the reference (Xu et al, 2020).…”

“…Huang et al (2015, 2016) deeply analyzed the vibration characteristics of a marine propulsion shaft through the coupled finite element method and experiment measurement. To foretell the transverse vibration characteristics of ship propulsion, Xu et al (2020) combined the boundary-smoothed Fourier series approach with the energy concept. Tian et al (2022) predicted the vibration characteristics of the podded propulsor shaft through an analytical approach.…”

Incrementally accumulated holographic SDP characteristic fusion method in ship propulsion shaft bearing fault diagnosis

“…In a ship propulsion shafting system (see figure 1), the intermediate bearing is one of the most important components because it is indispensable in realizing the transmission function [1]. A rolling bearing has the advantages of a simple structure and good load capacity, thereby enabling it to be widely used as an intermediate bearing in a ship propulsion shafting system.…”

Free Vibration Exploration of Rotating FGM Porosity Beams under Axial Load considering the Initial Geometrical Imperfection

“…Szymczak and Kujawa [14] presented an exact formulation of the frequency for free torsional vibration analysis of laminated beams subjected to axial load. Xu et al [15] used the energy principle in conjunction with the Rayleigh-Ritz procedure to investigate the flexural vibration and its power flow of an axially loaded beam with arbitrary boundary and nonuniform elastic foundation. Brahimi-Mamaghani et al [16] employed an analytical approach to finding the solution of dynamic and vibration stability of a viscoelastic FGM beam under axial load, where the Laplace transform and a Galerkin discretization scheme were combined to capture the solution.…”