分数导数粘弹性模型描述的土中管桩竖向振动的频域解

在分数导数粘弹性本构模型的基础上综合考虑桩周土和桩芯土的平衡方程和几何方程建立了桩周土和桩芯土的竖向运动的控制方程．在频率域内利用分离变量法和分数导数的性质求解了桩周土和桩芯土竖向振动控制方程．考虑管桩与桩周土、管桩与桩芯土的边界连续性条件以及三角函数的正交性得到了分数导数粘弹性模型描述的土中管桩的竖向振动，通过数值分析研究了管桩和土体模型参数和几何参数对管桩的桩顶复刚度的影响规律．结果显示：桩芯土本构模型的分数导数的阶数对管桩竖向振动的影响较桩周土本构模型的阶数要小，且与频率有一定关系；桩芯土与桩周土的模型参数比τ1 和τ2 对等效阻尼的影响较对刚度因子的影响要大；管桩桩周和桩芯的直径比d 越小，管桩复刚度的实部和虚部就越大；土体力学性能对管桩竖向振动的影响要比管桩桩身力学性能的影响小．

Vertical Vibration of Pipe Pile in Soil Described by Fractional Derivative Viscoelastic Model

The governing equations of vertical vibrations of the soil around the pile and the pile core soil are established based on fractional derivative viscoelastic constitutive model and considering the equilibrium equations and geometric equations of the soil around the pile and the pile core soil. The governing equations of vertical vibrations of the soil around the pile and the pile core soil are solved in the frequency domain by using the properties of fractional derivative and the separation of variable method. The vertical vibrations of pipe pile in soil described by fractional derivative viscoelastic model is obtained by considering the continuity boundary conditions between the soil around the pile, pile core soil and pipe pile and the orthogonality of trigonometric function, the influence laws of the model parameters and geometric models of pipe pile and soil on the complex stiffness at pipe pile top are studied by numerical analysis. The results show that the influence of the order of the fractional derivative of constitutive model of the pile core soil on the vertical vibration is smaller than the order of the fractional derivative constitutive model of the soil around the pile and the influence has a certain relationship with frequency, and the influence of the pile core soil and the soil around the pile model parameter ratio τ1 and τ2 on the equivalent damping is larger than on the stiffness factor, and the smaller the diameter ratio d of the soil around the pile and the pile core soil, the larger the real part and imaginary complex stiffness of the pipe pile, and the influence of the mechanical properties of the soil on the vertical vibration of the pipe pile is more smaller than the influence of mechanical properties of the pile body.