力学与实践 ›› 2020, Vol. 42 ›› Issue (6): 701-707.DOI: 10.6052/1000-0879-20-348

• 应用研究 • 上一篇    下一篇

旋转悬臂Rayleigh轴的Galerkin近似解1)

张玉环, 任勇生2), 张金峰   

  1. 山东科技大学机械电子工程学院,山东青岛 266590
  • 收稿日期:2020-08-17 修回日期:2020-09-14 出版日期:2020-12-20 发布日期:2020-12-20
  • 通讯作者: 2) 任勇生,教授,研究方向为系统动力学与振动控制。E-mail: renys@sdust.edu.cn
  • 基金资助:
    1) 国家自然科学基金资助项目(11672166)。

GALERKIN APPROXIMATE SOLUTIONS OF A ROTATING CANTILEVER RAYLEIGH SHAFT 1)

ZHANG Yuhuan, REN Yongsheng2), ZHANG Jinfeng   

  1. College of Mechanical and Electronic Engineering, Shandong University of Science and Technology,Qingdao 266590, Shandong, China
  • Received:2020-08-17 Revised:2020-09-14 Online:2020-12-20 Published:2020-12-20

摘要: 主要研究旋转悬臂Rayleigh轴的涡动频率和临界转速。基于Rayleigh 梁模型建立旋转悬臂Rayleigh轴的运动方程,通过Galerkin法将运动方程离散化,Galerkin 过程分别选择不旋转Euler--Bernoulli 轴的振型函数和旋转Rayleigh 轴的振型函数为试探函数,对不同方法得到的数值结果进行收敛性验证和对比分析,并且将其与涡动频率和临界转速的经典解 进行比较。结果表明,采用不旋转振型函数简单快捷,能够极大地方便计算过程,因此,将其用于近似求解旋转悬臂轴的动力学特性具有明显的优越性。

关键词: 旋转轴, 悬臂, 涡动频率, 临界转速, Galerkin法

Abstract: The whirling frequency and the critical speed of a rotating cantilever Rayleigh shaft are studied in this paper, based on the Rayleigh beam model, and the motion equation of the rotating cantilever Rayleigh shaft is derived, and discretized by the Galerkin method. During the Galerkin process, the modal shape functions of the non-rotating Euler-Bernoulli beam and the rotating Rayleigh beam with clamped-free boundary conditions are selected as the trial functions to obtain the whirling frequencies and the critical speeds. Both solutions are illustrated by numerical examples, the convergence of solutions is tested, and the results are compared with the classical solution obtained analytically. It is shown that using the modal shape of the non-rotating Euler-Bernoulli beam to obtain the approximation is usually far easier and faster than using the modal shape of the rotating Rayleigh beam. Therefore, it is preferred for the dynamic solution of the rotating cantilever shaft.

Key words: rotating shaft, cantilever, whirl frequencies, critical speeds, Galerkin method

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