粘性阻尼土中变截面桩的纵向振动特性与应用研究

考虑土体轴对称波动效应,对变截面桩在任意激振力作用下的纵向振动特性进行了研究。假定桩为竖直、弹性、变截面体,土为线性粘弹性体,其材料阻尼为粘性阻尼。利用拉普拉斯变换,将定解问题转化到拉普拉斯域内求解,通过引入势函数并结合阻抗函数的传递性,得到了拉普拉斯域内的桩顶阻抗函数解析解,进而可得到频域内的桩顶阻抗函数和速度导纳的解析解,利用卷积定理和傅里叶逆变换,求得了半正弦脉冲激振力作用下桩顶速度时域响应半解析解。基于所得解对桩的纵向振动特性进行了分析,重点讨论了桩身截面变化情况对速度导纳曲线和反射波曲线的影响,得到了许多重要结论。

Study on longitudinal vibration of pile with variable sections in the viscous damping soil and its applications

Modeling soil as an axisymmetric continuum and taking its axisymmetric wave effect into account,longitudinal vibration of pile with variable sections undergoing arbitrary load is theoretically investigated.The pile is assumed to be vertical,elastic and of variable sections,and the soil is a linear visco-elastic layer with viscous damping.With Laplace transforms,the question can be solved in Laplace domain.With the aid of two potentials in conjunction with impedance transmit functions,an analytical solution for the impedance function in Laplace domain is yielded,so are the corresponding analytical solutions for the impedance function and mobility at the level of the pile head in frequency domain.With the convolution theorem and inverse Fourier transform,a semi-analytical solution of velocity response in time-domain subjected to a semi-sine exciting force is derived.Based on the solutions proposed herein,the influence on mobility curves and reflection wave curves caused by variety of sections are emphatically discussed.Some important conclusions are drawn.