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梁在固有振动中的对偶关系

胡海岩

胡海岩. 梁在固有振动中的对偶关系[J]. 力学学报, 2020, 52(1): 139-149. doi: 10.6052/0459-1879-20-019
引用本文: 胡海岩. 梁在固有振动中的对偶关系[J]. 力学学报, 2020, 52(1): 139-149. doi: 10.6052/0459-1879-20-019
Hu Haiyan. DUALITY RELATIONS OF BEAMS IN NATURAL VIBRATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 139-149. doi: 10.6052/0459-1879-20-019
Citation: Hu Haiyan. DUALITY RELATIONS OF BEAMS IN NATURAL VIBRATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 139-149. doi: 10.6052/0459-1879-20-019

梁在固有振动中的对偶关系

doi: 10.6052/0459-1879-20-019
基金项目: 1) 国家自然科学基金重点资助项目(11832005)
详细信息
    通讯作者:

    胡海岩

  • 中图分类号: O313

DUALITY RELATIONS OF BEAMS IN NATURAL VIBRATIONS

  • 摘要: 本文研究具有齐次边界的Euler-Bernoulli梁在固有振动中的对偶关系.将两种截面变化不同、但固有频率完全相同的梁定义为异截面对偶梁.通过位移描述和弯矩描述,指出具有齐次边界条件的变截面梁共有如下7类异截面对偶:一是自由-自由梁与固支-固支梁,二是滑支-自由梁与滑支-固支梁(及其镜像),三是铰支-自由梁与铰支-固支梁(及其镜像),四是铰支-滑支梁与铰支-滑支梁(及其镜像),五是滑支-滑支梁与滑支-滑支梁,六是铰支-铰支梁与铰支-铰支梁,七是固支-自由梁与自由-固支梁.在此基础上,将两种截面变化相同、固有频率也相同的梁定义为同截面对偶梁.研究表明,当且仅当梁的截面积函数和截面惯性矩函数具有特定指数函数形式时,前4类异截面对偶梁能成为同截面对偶梁.对于等截面梁,上述前3类同截面对偶仍可保持,而第4类同截面对偶退化为彼此镜像.此时,通过引入转角描述可发现等截面梁产生新对偶,即滑支-滑支梁与铰支-铰支梁对偶.上述等截面梁的对偶均具有如下特征,即对偶中的一种梁具有静定约束,另一种梁具有静不定约束.

     

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出版历程
  • 收稿日期:  2020-01-11
  • 刊出日期:  2020-02-10

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