东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2008, Vol. 29 ›› Issue (10): 1463-1466.DOI: -

• 论著 • 上一篇    下一篇

中间支承梁的发散/颤振失稳

荆洪英;金基铎;闻邦椿;   

  1. 东北大学机械工程与自动化学院;沈阳航空工业学院航空宇航工程学院;
  • 收稿日期:2013-06-22 修回日期:2013-06-22 出版日期:2008-10-15 发布日期:2013-06-22
  • 通讯作者: Jing, H.-Y.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(50535010)

Divergence/flutter of the beam with intermediate support

Jing, Hong-Ying (1); Jin, Ji-Duo (2); Wen, Bang-Chun (1)   

  1. (1) School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China; (2) School of Aviation and Astronavigation Engineering, Shenyang Institute of Aeronautical Engineering, Shenyang 110136, China
  • Received:2013-06-22 Revised:2013-06-22 Online:2008-10-15 Published:2013-06-22
  • Contact: Jing, H.-Y.
  • About author:-
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摘要： 研究了一端简支另一端轴向受压具有中间支承梁的振动.推导了此梁弯曲振动的频率方程及振型函数的解析表达式.根据频率方程讨论了中间支承位置变化对梁固有频率的影响.应用Ritz-Galerkin方法,采用梁的前三阶振型对梁的运动微分方程进行离散化处理,得到了梁在不同中间支承位置处的失稳临界压力.发现了在梁上存在一个特殊的中间支承位置lξ,随着压力P从零开始增加,当中间支承位置ξblξ时,则梁先发生发散失稳.

关键词: 中间支承梁, 固有频率, 振型函数, 发散, 颤振

Abstract: The vibration of a beam which is simply supported at one end, resting on a support at some intermediate location, and has the other end subjected to an axial force is studied. The characteristic equation of the beam is derived, as well as an analytic expression of its eigenfunction. Then based on the characteristic equation, the effect of the position of intermediate support on the natural frequencies of the beam is discussed. The differential equation of the beam's motion is discretized applying the first three eigenfunctions by Ritz-Galerkin method, thus getting the critical axial force for the beam destabilization when the intermediate support is positioned differently. It is found that there is a special position of intermediate support ξl, as the axial load P increases, for location of intermediate support ξb < ξl, the beam becomes unstable by flutter, and for ξb > ξl, it loses stability by divergence.

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