任意段变模量桩纵向振动的解析解

建立了均质土中考虑桩端土和桩侧土作用的任意段变模量桩，讨论了在桩顶受纵向激励时的定解问题，并用拉氏变换（Laplace)求得桩顶速度频域响应的解析解，然后利用卷积定理和拉氏逆变换求得桩顶速度时域响应的解析解，并将其运用到桩基质量的动力检测中。对弹性模量突变桩以及模量连续变化桩的振动特性作了进一步的研究，并将理论曲线与实测曲线进行了拟合对比，结果表明，两者吻合较好。

AN ANALYTICAL SOLUTION TO LONGITUDINAL VIBRATION OF A PILE OF ARBITRARY SEGMENTS WITH VARIABLE MODULUS

The vibration problem of a pile of arbitrary segments with variable modulus under exciting force is established, in which the influence of the soil under pile toe and the surroundings is taken into account. With Laplace transforms, the transmit functions for velocity and displacement of the pile are derived. Furthermore, in terms of the convolution theorem and inversed Laplace transform, an analytical solution for the time domain response of a pile subjected to a semi-sine impulse is developed, which is the theoretical basis of the sonic method in pile integrity testing. Based on the solution, the vibration properties of a pile with sharp or continuous variation in modulus are studied. The validity of this approach is verified through field dynamic tests on some engineering piles. It shows that the theoretical prediction agrees well with the actual response of the pile are in good agreement.