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借助分数导数理论、粘弹性理论和土动力学理论建立了三维轴对称条件下分数导数粘弹性土层的水平振动控制方程,采用势函数和分离变量法求解了分数导数粘弹性土层的水平振动,得到了土层的水平动力阻抗。并借助于桩-土界面的连续条件和三角函数的正交性得到了分数导数粘弹性土层中单桩的水平动力阻抗。通过数值算例研究了桩土参数对分数导数粘弹性土层水平动力阻抗因子和土层中单桩水平动力阻抗的影响。研究表明:分数导数粘弹性土层的水平动力阻抗因子和分数导数粘弹性土层中桩顶水平动力阻抗可以退化为经典粘弹性和弹性土层的情况;桩土模量比对分数导数粘弹性土层中桩顶水平动力阻抗的影响与弹性情况存在较大差异。
Based on fractional derivative theory, viscoelastic theory and soil dynamics theory, the horizontal vibration governing equations of fractional derivative viscoelastic soil under three-dimensional axisymmetric conditions are established. The potential vibration and separation variables are used to solve the horizontal vibration of fractional derivative viscoelastic soil , Got the level of the soil dynamic impedance. The horizontal dynamic impedance of single pile in fractional derivative viscoelastic soil is obtained by means of the continuous condition of pile-soil interface and the orthogonality of trigonometric function. The influence of pile-soil parameters on the horizontal dynamic impedance of fractional-derivative viscoelastic soil and on the horizontal dynamic impedance of single pile in soil are studied by numerical examples. The results show that the horizontal dynamic impedance factor of fractional derivative viscoelastic soil and the horizontal dynamic impedance of pile top in fractional derivative viscoelastic soil can degenerate into the classical viscoelastic and elastic soil. The ratio of pile-soil modulus to fractional derivative viscoelasticity The effect of horizontal dynamic impedance of pile top in soil layer and its elastic condition are quite different.