一维分数导数粘弹性饱和多孔介质层的稳态响应

STEADY STATE RESPONSE OF ONE-DIMENSION LIQUID-SATURATED POROUS MEDIUM USING FRACTIONAL DERIVATIVE VISCOELASTIC MODEL

固相骨架的应力-应变关系利用分数导数粘弹性Kelvin模型来描述,在流相和固相微观不可压以及小变形的假定下建立了分数导数粘弹性饱和多孔介质层一维稳态响应的数学模型和运动控制方程,求得了分数导数粘弹性饱和多孔介质层一维稳态响应的固相位移和液相位移。通过数值算例分析了分数导数的阶数对稳态响应的影响。研究结果表明:固相位移和液相位移随频率的增大逐渐趋于零,在低频时,分数导数的阶数越大固相位移和液相位移越大。

The stress-strain relationship of a solid skeleton is described by a fractional derivative Kelvin viscoelastic model, and the mathematic model and equations of motion of the steady state response of one-dimension liquid-saturated porous medium are established, in which the saturated porous material is modeled as a two phase system composed of an incompressible solid phase and an incompressible fluid phase, and the displacements both of the solid phase and fluid phase in one dimension liquid saturated porous medium described by fractional derivative viscoelastic model are obtained. The influence of fractional order on the steady state response is analyzed by a numerical example. The result indicates that the displacements both of solid phase and fluid phase will decrease to zero with the increase of frequency, and the displacements both of solid phase and fluid phase increase with the increase of fractional order at lower frequencies.