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饱和多孔弹性Timoshenko悬臂梁的动、静力弯曲

杨骁 文群

杨骁, 文群. 饱和多孔弹性Timoshenko悬臂梁的动、静力弯曲[J]. 应用数学和力学, 2010, 31(8): 949-960. doi: 10.3879/j.issn.1000-0887.2010.08.008
引用本文: 杨骁, 文群. 饱和多孔弹性Timoshenko悬臂梁的动、静力弯曲[J]. 应用数学和力学, 2010, 31(8): 949-960. doi: 10.3879/j.issn.1000-0887.2010.08.008
YANG Xiao, WEN Qun. Dynamic and Quasi-Static Bending of Saturated Poroelastic Timoshenko Cantilever Beam[J]. Applied Mathematics and Mechanics, 2010, 31(8): 949-960. doi: 10.3879/j.issn.1000-0887.2010.08.008
Citation: YANG Xiao, WEN Qun. Dynamic and Quasi-Static Bending of Saturated Poroelastic Timoshenko Cantilever Beam[J]. Applied Mathematics and Mechanics, 2010, 31(8): 949-960. doi: 10.3879/j.issn.1000-0887.2010.08.008

饱和多孔弹性Timoshenko悬臂梁的动、静力弯曲

doi: 10.3879/j.issn.1000-0887.2010.08.008
基金项目: 国家自然科学基金资助项目(10872124)
详细信息
    作者简介:

    杨骁(1965- ),男,山西运城人,教授,博士生导师(联系人.Tel/Fax:+86-21-56331519;E-mail:xyang@shu.edu.cn).

  • 中图分类号: O321;O357.3

Dynamic and Quasi-Static Bending of Saturated Poroelastic Timoshenko Cantilever Beam

  • 摘要: 在经典单相Timoshenko梁变形和孔隙流体仅沿饱和多孔弹性梁轴向运动的假定下,基于不可压饱和多孔介质的三维Gurtin型变分原理,首先建立了饱和多孔弹性Timoshenko悬臂梁动力响应的一维数学模型.在若干特殊情形下,该模型可分别退化为饱和多孔弹性梁的Euler-Bernoulli模型、Rayleigh模型和Shear模型等.其次,利用Laplace变换,分析了固定端不可渗透、自由端可渗透的饱和多孔弹性Timoshenko悬臂梁在自由端阶梯载荷作用下的动静力响应,给出了梁自由端处挠度随时间的响应曲线,考察了固相与流相相互作用系数、梁长细比等参数对悬臂梁动静力行为的影响.结果表明:饱和多孔弹性梁的拟静态挠度具有与粘弹性梁挠度类似的蠕变特征.在动力响应中,随着梁长细比的增大,自由端挠度的振动周期和幅值增大,且趋于稳态值的时间增长,而随着两相相互作用系数的增大,梁挠度振动衰减加快,并最终趋于经典单相弹性Timoshenko梁的静态挠度.
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出版历程
  • 收稿日期:  1900-01-01
  • 修回日期:  2010-06-27
  • 刊出日期:  2010-08-15

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