Abstract: Regarding the soil portion below the floating pile as a virtual soil pile, and the soil around the pile as a fractional derivative viscoelastic medium, the vertical vibration of the floating pile was solved. The boundary conditions of the soil and the pile and their continuity conditions were considered. The influence of main mechanical parameters of the pile and the soil on the complex stiffness at the head of the floating pile was investigated. The result indicates that the order of the fractional derivative has some influence on the real part and imaginary part of the complex stiffness. The constraint effect of the soil on the pile will be larger when the length of the pile is longer. The real part of the complex stiffness at the pile head will decrease when the model’s constitutive parameter increases. And the influence of the model’s constitutive parameter on the imaginary part of the complex stiffness is somewhat complicated.

Key words: vibration and wave , vertical vibration , floating pile , virtual pile , fractional derivative , analytical solution

摘要： 将桩底下部土体视为虚拟土桩，桩周土体视为分数阶黏弹性介质，通过考虑桩土边界条件和连续条件，求解分数阶黏弹性土中悬浮桩的纵向振动响应。分析主要桩土力学参量对悬浮桩桩顶复刚度的影响。结果表明：分数导数的阶数对桩顶复刚度的实部和虚部有一定的影响，桩长越长土体对桩基的约束越大，本构模型参数越大，桩顶复刚度的实部越小，而模型参数对复刚度虚部的影响较为复杂。

关键词: 振动与波, 纵向振动, 悬浮桩, 虚拟桩, 分数导数, 解析解