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基于土动力学、黏弹性理论和分数阶导数理论建立了分数阶三维积分型黏弹性土体水平振动控制方程。利用势函数对分数阶三维积分型黏弹性土体的水平振动方程进行解耦,借助分离变量法在频率内求解了分数阶三维积分型黏弹性土体的水平振动,得到了土体对单桩的水平作用,进而建立了分数阶三维积分型黏弹性土体中单桩的水平振动方程。考虑单桩的边界条件和桩顶水平动力阻抗的定义,求解了单桩的水平振动,并对桩顶水平动力阻抗进行了数值分析和讨论。研究表明:高频时,分数导数的阶数对水平动力阻抗有影响,土体黏性系数较小时水平动力阻抗实部和虚部随频率的变化曲线存在波动现象;长径比越大,水平动力阻抗越小,长径比达到一定程度时其对水平动力阻抗几乎没有影响。
Based on soil dynamics, viscoelasticity theory and fractional derivative theory, the governing equations of fractional 3D viscoelastic soil horizontal vibration are established. Using the potential function to decouple the horizontal vibration equations of fractional three-dimensional viscoelastic soils, the horizontal vibration of fractional three-dimensional viscoelastic soils is solved in frequency by the method of separation variables. Then the horizontal vibration equation of single pile in three-dimensional integral viscoelastic soil is established. Considering the boundary condition of single pile and the definition of horizontal dynamic impedance of pile top, the horizontal vibration of single pile is solved and the horizontal dynamic impedance of pile top is analyzed and discussed. The results show that the order of fractional derivative has an influence on the horizontal dynamic impedance at high frequency, and the fluctuation of the real and imaginary part of the horizontal dynamic impedance fluctuates with the frequency when the soil viscosity coefficient is small. The larger the aspect ratio, The smaller the dynamic impedance, the smaller the aspect ratio has a certain extent, it has almost no effect on the horizontal dynamic impedance.