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粘弹土体的应力-应变关系利用分数导数粘弹性模型进行描述,建立了分数导数粘弹性土层的竖向振动控制方程。在考虑三维波动的条件下,利用势函数和分离变量的方法求解了分数导数粘弹性土层的竖向振动。考虑桩土边界条件和接触条件对分数导数粘弹性土中桩基的竖向振动进行了研究,分析了主要桩土力学参数对桩顶复刚度和导纳的影响规律。研究表明:分数导数的阶数、土体模型参数和桩长径比对桩顶复刚度和导纳有较大影响;分数导数粘弹性模型可以在较大的范围内较精确地描述土体的力学行为;当长径比增大到一定的程度时再增加长径比对桩基竖向振动特性的影响不大。
The stress-strain relationship of viscoelastic soil is described by means of fractional-derivative viscoelastic model, and the governing equation of vertical vibration of fractional-derivative viscoelastic soil is established. Taking into account the three-dimensional fluctuations, the vertical vibration of fractional derivative viscoelastic soil is solved by using the potential function and the separation of variables. The vertical vibration of pile foundation in fractional derivative viscoelastic soil is considered considering the boundary conditions and contact conditions of pile-soil. The influence of main pile-soil mechanical parameters on the complex stiffness and admittance of pile top is analyzed. The results show that: the order of fractional derivative, soil model parameters and pile aspect ratio have a great influence on the complex stiffness and admittance of pile top; Fractional derivative viscoelastic model can describe soil mass more accurately Mechanical behavior. When the aspect ratio increases to a certain extent, increasing the aspect ratio has little effect on the vertical vibration characteristics of pile foundation.