不可压饱和多孔弹性梁、杆动力响应的数学模型

MATHEMATICAL MODEL FOR DYNAMICS OF INCOMPRESSIBLE SATURATED POROELASTIC BEAM AND ROD~

基于多孔介质理论,首先建立了饱和多孔弹性杆件弯曲与轴向变形时动力响应的数学模型.其次,基于多孔弹性梁弯曲变形的数学模型,利用Laplace变换,分析了两端可渗透的饱和多孔弹性悬臂梁在自由端受阶梯载荷作用下的动静力响应,给出了梁弯曲时挠度、弯矩以及孔隙流体压力等效力偶等物理量随时间的响应曲线.发现不可压多孔弹性梁的拟静态响应亦存在Mandel-Cryer现象,多孔弹性梁的挠度具有与粘弹性梁挠度类似的蠕变特征,然而,其应力响应不同于粘弹性梁,随着时间的增加,梁拟静态响应的弯矩逐渐增加,并达到一个稳态值.这些结果有助于揭示植物根茎等力学行为的机理.

Based on the theory of porous media,the,mathematical models for dynamics of the fluid-saturated poroelastic beams and rods are established. Then the dynamical/ quasi-static behavior of the poroelastic cantilever beam subjected to a step load at the free end,with permeable at two ends,is investigated by the Laplace transformation. The variations of the deflections,bending moments of the poroelastic beam and the equivalent couples of the pore fluid pressure are analyzed for different material parameters. It can be seen that the Mandel-Cryer phenomenon also occurs in the quasi-static deformations of the poroelastic cantilever beam. Furthermore,the deflections of the poroelastic beam possess the creep behavior similar to deflections of viscoelastic beam. Nevertheless,the bending moment of the quasi-static poroelastic cantilever beam is increased with time and finally approaches to a steady value. This is different from the behavior of the bending moment of the viscoelastic beam. The results presented here are helpful for revealing the mechanism of the mechanical behavior of roots and stems of plants.