带承台单桩耦合体系纵向振动的重正化解法研究

 从非线性振动力学的角度出发，基于重正化方法研究非均匀地层中带承台单桩耦合体系的纵向自由振动问题。采用弹簧耦合单元块体的形式对单桩及桩侧土体进行离散，并用广义Voigt串联体描述黏弹性土层的摩阻效应，建立多段多自由度非线性承台–单桩–土纵向振动模型。通过重正化坐标转换原则给出振动模型的纵向振动频率解，并引入质量参振分配系数对不同情况下的振动频率方程进行表征，进而通过算例验证重正化解法的正确性和准确性。最后考察桩身质量、材料刚度、承台质量及桩侧摩阻力对耦合体系自由振动频率的影响规律，研究成果可为带承台桩基础动力设计提供参考。

Renormalization study of vertical vibration of single pile with cushion cap

From the perspective of nonlinear vibration mechanics，the vertical free vibration characteristics of a single pile with cushion cap embedded in layered foundation were studied based on renormalization method. The form of the spring coupled with the unit block was taken to discretize the pile body and its surrounding soil. The generalized Voigt series were used to describe the friction effect of the viscoelastic soil layers. A vertical vibration model for the nonlinear system of cushion cap-single pile-soil with multiple degrees of freedom was established. The vertical vibration frequency of the coupled model was given through the coordinate transformation principle of renormalization and the distribution coefficient of pile quality was introduced to represent different equations of vibration frequency under different conditions. The correctness and accuracy of the renormalization method for vibration frequency equations were verified. The influential factors including the pile quality，the material stiffnessthe cap quality and the friction resistance were investigated.