梁在固有振动中的对偶关系

Haiyan Hu*

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

3 引用 (Scopus)

摘要

The duality relations are studied in the paper for the Euler-Bernoulli beams with homogeneous boundaries in natural vibrations. A pair of beams is first defined as a dual of different cross-sections if they have the same natural frequencies, but different variations of cross-sections. The duals of different cross-sections are analyzed via a dual of displacement description and bending moment description, and the non-uniform beams with homogeneous boundaries can be classified as the following seven duals. They are (1) the dual of a free-free beam and a clamped-clamped beam, (2) the dual of a slipping-free beam and a slipping-clamped beam (and their mirrors), (3) the dual of a hinged-free beam and a hinged-clamped beam (and their mirrors), (4) the dual of two hinged-slipping beams, (5) the dual of two slippingslipping beams, (6) the dual of two hinged-hinged beams, and (7) the dual of a clamped-free beam and a free-clamped beam. Then, a pair of beams is defined as a dual of identical cross-sections if they have the same natural frequencies and the same variations of cross-sections. It is proved that the first four duals of different cross-sections become the duals of identical cross-sections if and only if the area of cross-section and the inertial moment of cross-section of any beam in those duals take a specific form of exponential function. Afterwards, the first three duals of identical cross-sections are verified to keep the dual relations for uniform beams, whereas the fourth dual is degenerated to a pair of mirrors. Based on the dual of displacement description and slope description, a new dual of uniform beams is found for a slipping-slipping beam and a hinged-hinged beam. Finally presented is an important feature of all the duals of uniform beams. That is, one uniform beam in a dual has statically determinate constraints while the other uniform beam in the same dual has statically indeterminate constraints.

投稿的翻译标题Duality relations of beams in natural vibrations
源语言繁体中文
页(从-至)139-149
页数11
期刊Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics
52
1
DOI
出版状态已出版 - 18 1月 2020

关键词

  • Description of bending moment
  • Description of slope
  • Dual
  • Natural vibration
  • Non-uniform beam
  • Uniform beam

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引用此

Hu, H. (2020). 梁在固有振动中的对偶关系. Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics, 52(1), 139-149. https://doi.org/10.6052/0459-1879-20-019