Dynamic and Quasi-Static Bending of Saturated Poroelastic Timoshenko Cantilever Beam
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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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关键词:
- 饱和多孔介质理论 /
- 饱和多孔Timoshenko梁 /
- 数学模型 /
- Laplace变换 /
- 动静力弯曲
Abstract: Based on the three-dmiensional Gurtin-type variational principle of the incompressible saturated porousmedia, first, a one-dimensionalm athematical model for dynamics of the saturated poroelastic Timoshenko Cantilever beam was established with a ssumptions of deformatin of the classical single phase Tmioshenko beam and the movement of pore fluid only in the axial direction of the saturated poroelasic beam. This mathematical model can be degene rated into the Euler-Bernoullim odel, Rayleigh model and Shear model of the saturated poroelastic beam, respe ctively, under some specialcases. Secondly, dynamic and quasi-static behavior of a saturated poroelastic Tmioshenko cant ilever beam with mipermeable and permeable at its fixed and free end, respectively, subjected to a step load at its free end, was analyzed by the Laplace transform. The variations of the deflections at the beam free end against the tmie were shown in figures, and the influences of the in teraction coefficient between the porefluid and solid skele to naswellas the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam were examined. It is shown that the quasi-static deflections of the saturated poroela stic beam possess the creep behavior smiilar to that of viscoelastic beam. In dynamic responses, with the slenderness ratio increasing, the vibration periods and amplitudes of the deflections at the free end increase, and the tmie needed for deflections to approachits stationary values also increases. Whereas, with the interaction coefficient increasing, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Tmioshenko beam. -
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