• CN:11-2187/TH
  • ISSN:0577-6686

›› 2005, Vol. 41 ›› Issue (1): 226-229.

• 论文 • 上一篇    下一篇

求解复杂轴扭振动力特性的一种近似分析方法

楼梦麟;严国香;李建元   

  1. 同济大学土木工程防灾国家重点实验室
  • 发布日期:2005-01-15

APPROACH TO SOLVE TORSIONAL VIBRATION DYNAMIC CHARACTERISTICS OF COMPLICATED SHAFT

Lou Menglin;Yan Guoxiang;Li Jianyuan   

  1. State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University
  • Published:2005-01-15

摘要: 应用模态摄动法求解非均质变截面复杂轴的扭转振动的模态特性。在这一方法中,选择与复杂轴约束条件相同、等截面均匀轴的扭转振动解析模态函数作为近似分析的基函数,采用Ritz展开和摄动分析相结合的方法,把复杂轴扭振的变系数微分方程的求解,转化为一组代数方程组的求解。虽然这一方法应用了结构振动分析中常用的Ritz展开原理,但避免了关于模态广义坐标的特征值问题的求解,通过代数方程组的求解,可逐一求得复杂轴的扭转振动的模态特性,简化了求解的难度。通过2个算例的分析表明,该方法简单实用,且具有较高的精度。

关键词: 非均质变截面轴, 模态摄动法, 模态特性, 扭转振动

Abstract: The modal perturbation method is introduced to solve the modal characteristics of torsional vibration of a complicated nonhomogeneous shaft with variable cross-section. In this method, the analytical modal functions of the homogeneous shaft with uniform cross-section along its length, which has same end boundary conditions with the complicated shaft, are chosen as the basic functions for the approximate solution. By applying the Ritz expansion and the perturbation analysis, to solve the partial differential equation with variable coefficient is transferred into solving a set of the algebraic equations. Although the Ritz expansion that is often used in dynamic analysis of structures is applied in the suggested method, the eigenvalue problem of the Ritz generalized coordinates can be avoided. The modal characteristics of torsional vibration of the complicated shaft can be obtained by solving the algebraic equations one by one. It is shown by two numerical examples that the simplified method can be applied easily and has high precision.

Key words: Modal characteristics, Modal perturbation method, Nonhomogeneous shaft with variable cross-section, Torsional vibration

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